RandomVariate—Wolfram Language Documentation

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RandomVariate[dist, n] gives a list of n pseudorandom variates from the symbolic distribution dist. RandomVariate[dist, {n1, n2, ...}] gives an n 1* n 2*... array of pseudorandom variates from the symbolic distribution dist." /> <link rel="stylesheet" href="//www.wolframcdn.com/fonts/source-code-pro/1.0/all.css"> <link rel="stylesheet" href="/language-assets/css/global.css"> <link rel="stylesheet" href="/language-assets/css/iconography.css"> <link rel="stylesheet" href="/language-assets/css/in-out.css"> <link rel="stylesheet" href="/language-assets/css/header-language.css"> <link rel="stylesheet" href="/language-assets/css/icons.css"> <link rel="stylesheet" href="/language-assets/css/entities.css"> <link rel="stylesheet" href="/language-assets/css/language.css"> <link rel="stylesheet" href="/language-assets/css/root-guide-language.css"> <link rel="stylesheet" href="/language-assets/css/special-styles.css"> <link rel="stylesheet" href="/language-assets/css/language-specific.css"> <link rel="stylesheet" href="/language-assets/css/man-page.css"> <link rel="stylesheet" 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href="/language/ref/RandomReal.html"><span class="dropdownPad">RandomReal</span></a> </li> <li> <a class="sub-ref" href="/language/ref/RandomComplex.html"><span class="dropdownPad">RandomComplex</span></a> </li> <li> <a class="sub-ref" href="/language/ref/RandomPoint.html"><span class="dropdownPad">RandomPoint</span></a> </li> <li> <a class="sub-ref" href="/language/ref/RandomGeoPosition.html"><span class="dropdownPad">RandomGeoPosition</span></a> </li> <li> <a class="sub-ref" href="/language/ref/RandomFunction.html"><span class="dropdownPad">RandomFunction</span></a> </li> <li> <a class="sub-ref" href="/language/ref/RandomGraph.html"><span class="dropdownPad">RandomGraph</span></a> </li> <li> <a class="sub-ref" href="/language/ref/RandomImage.html"><span class="dropdownPad">RandomImage</span></a> </li> <li> <a class="sub-ref" href="/language/ref/RandomInstance.html"><span class="dropdownPad">RandomInstance</span></a> </li> </ul> </li> <li> <a href="#" class="menu related-guides">Related Guides</a> <ul class="sub_menu"> <li> <a href="/language/guide/RandomVariables.html"><span class="dropdownPad">Random Variables</span></a> </li> <li> <a href="/language/guide/RandomNumberGeneration.html"><span class="dropdownPad">Random Number Generation</span></a> </li> <li> <a href="/language/guide/ProbabilityAndStatistics.html"><span class="dropdownPad">Probability & Statistics</span></a> </li> <li> <a href="/language/guide/MatrixDistributions.html"><span class="dropdownPad">Matrix Distributions</span></a> </li> <li> <a href="/language/guide/MatricesAndLinearAlgebra.html"><span class="dropdownPad">Matrices and Linear Algebra</span></a> </li> <li> <a href="/language/guide/ProbabilityWithQuantities.html"><span class="dropdownPad">Probability & Statistics with Quantities</span></a> </li> <li> <a href="/language/guide/ScientificModels.html"><span class="dropdownPad">Scientific Models</span></a> </li> <li> <a href="/language/guide/Statistics.html"><span class="dropdownPad">Statistical Data Analysis</span></a> </li> <li> <a href="/language/guide/RandomGraphs.html"><span class="dropdownPad">Random Graphs</span></a> </li> <li> <a href="/language/guide/Reliability.html"><span class="dropdownPad">Reliability</span></a> </li> <li> <a href="/language/guide/ActuarialComputation.html"><span class="dropdownPad">Actuarial Computation</span></a> </li> </ul> </li> </ul></nav><div class="main-heading"><h1 class="main-title">RandomVariate</h1><div class="iconography" data-src="s= d= m= c= u= l= n= e="></div></div><div class="functionIntroWrap"> <div class="functionIntro"> <p class="code clipboard-inline" data-code="Files/RandomVariate.en/usage_1.txt"> <span class="IF"><a href="/language/ref/RandomVariate.html">RandomVariate</a><span class="openbracket">[</span><span class="TI">dist</span><span class="closebracket">]</span></span> </p> <p class="code-description">gives a pseudorandom variate from the symbolic distribution <span class="IF"><span class="TI">dist</span></span>.</p> </div> <div class="functionIntro"> <p class="code clipboard-inline" data-code="Files/RandomVariate.en/usage_2.txt"> <span class="IF"><a href="/language/ref/RandomVariate.html">RandomVariate</a><span class="openbracket">[</span><span class="TI">dist</span><span class="comma">,</span><span class="TI">n</span><span class="closebracket">]</span></span> </p> <p class="code-description">gives a list of <span class="IF"><span class="TI">n</span></span> pseudorandom variates from the symbolic distribution <span class="IF"><span class="TI">dist</span></span>.</p> </div> <div class="functionIntro"> <p class="code clipboard-inline" data-code="Files/RandomVariate.en/usage_3.txt"> <span class="IF"><a href="/language/ref/RandomVariate.html">RandomVariate</a><span class="openbracket">[</span><span class="TI">dist</span><span class="comma">,</span><span class="openbrace">{</span><span class="TI">n</span><sub><span class="TR">1</span></sub><span class="comma">,</span><span class="TI">n</span><sub><span class="TR">2</span></sub><span class="comma">,</span><span class="TR"><span class="special-character Ellipsis">…</span></span><span class="closebrace">}</span><span class="closebracket">]</span></span> </p> <p class="code-description">gives an <span class="IF"><span class="TI"><span class="TI">n</span><sub><span class="TR">1</span></sub></span><span class="special-character Times">×</span><span class="TI"> </span><span class="TI"><span class="TI">n</span><sub><span class="TR">2</span></sub></span><span class="special-character Times">×</span><span class="TR"><span class="special-character Ellipsis">…</span></span></span> array of pseudorandom variates from the symbolic distribution <span class="IF"><span class="TI">dist</span></span>.</p> </div> </div><section id="DetailsAndOptions"><div class="inner"> <h1 class="toggle">Details and Options</h1> <div class="NotesThumbnails"> <img src="Files/RandomVariate.en/details_1.png" height="32" width="171" alt="" /> </div> <div class="hideable"> <ul class="functionList"> <li><a name="144922674"></a><span class="IF"><a href="/language/ref/RandomVariate.html">RandomVariate</a></span> can generate random variates for continuous, discrete, or mixed distributions specified as a symbolic distribution.</li> <li><a name="11251"></a><span class="IF"><a href="/language/ref/RandomVariate.html">RandomVariate</a></span> gives a different sequence of pseudorandom numbers whenever you run the Wolfram Language. You can start with a particular seed using <span class="IF"><a href="/language/ref/SeedRandom.html">SeedRandom</a></span>. </li> <li><a name="312064958"></a>With the setting <span class="IF"><a href="/language/ref/WorkingPrecision.html">WorkingPrecision</a>-><span class="TI">p</span></span>, random numbers of precision <span class="IF"><span class="TI">p</span></span> will be generated. </li> </ul> </div> </div></section><section id="Examples"><h1 id="1146015747" class="toggle open">Examples</h1><span class="open-all on">open all</span><span class="close-all">close all</span><div class="hideable"> <div> <h2 id="305829886" class="toggle open">Basic Examples<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(5)</span></h2> <div class="hideable"> <p><a name="33168379"></a>Simulate a continuous probability distribution:</p> <div id="67015906" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_1.png" data-in-width="235" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-bd6n28" data-code="Files/RandomVariate.en/i_1.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_1.png" data-out-width="50" data-out-height="18" ></div> <div id="980116677" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_2.png" data-in-width="341" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-qhtk5j" data-code="Files/RandomVariate.en/i_2.txt" ></div> <div id="1621417849" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_3.png" data-big="428 58" data-small="428 58" data-link="https://wolfram.com/xid/0b8dsol2sb-03mwaz" data-code="Files/RandomVariate.en/i_3.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_2.png" data-out-width="241" data-out-height="150" ></div> <div class="ExLine"><a name="238042897"></a></div> <p><a name="262168215"></a>Simulate a discrete probability distribution:</p> <div id="305936421" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_4.png" data-in-width="266" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-fcfkb7" data-code="Files/RandomVariate.en/i_4.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_3.png" data-out-width="132" data-out-height="18" ></div> <div id="300690354" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_5.png" data-in-width="336" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-e9a4f4" data-code="Files/RandomVariate.en/i_5.txt" ></div> <div id="678916680" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_6.png" data-in-width="330" data-in-height="78" data-link="https://wolfram.com/xid/0b8dsol2sb-lihtqy" data-code="Files/RandomVariate.en/i_6.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_4.png" data-out-width="241" data-out-height="153" ></div> <div class="ExLine"><a name="484010912"></a></div> <p><a name="18672103"></a>Simulate a multivariate continuous distribution:</p> <div id="15282553" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_7.png" data-in-width="282" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-jdudn" data-code="Files/RandomVariate.en/i_7.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_5.png" data-out-width="371" data-out-height="35" ></div> <div id="70178788" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_8.png" data-in-width="352" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-bf2gk2" data-code="Files/RandomVariate.en/i_8.txt" ></div> <div id="91636799" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_9.png" data-big="496 39" data-small="496 39" data-link="https://wolfram.com/xid/0b8dsol2sb-bsudox" data-code="Files/RandomVariate.en/i_9.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_6.png" data-out-width="321" data-out-height="133" ></div> <div class="ExLine"><a name="29668214"></a></div> <p><a name="46596737"></a>Simulate a multivariate discrete distribution:</p> <div id="726159820" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_10.png" data-in-width="374" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-mamese" data-code="Files/RandomVariate.en/i_10.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_7.png" data-out-width="172" data-out-height="18" ></div> <div id="276520704" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_11.png" data-big="443 19" data-small="443 19" data-link="https://wolfram.com/xid/0b8dsol2sb-euw20y" data-code="Files/RandomVariate.en/i_11.txt" ></div> <div id="272332230" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_12.png" data-big="453 58" data-small="453 58" data-link="https://wolfram.com/xid/0b8dsol2sb-esfa6g" data-code="Files/RandomVariate.en/i_12.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_8.png" data-out-width="261" data-out-height="107" ></div> <div class="ExLine"><a name="779020577"></a></div> <p><a name="133416279"></a>Generate random numbers from a mixture distribution:</p> <div id="244138734" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_13.png" data-in-width="395" data-in-height="39" data-link="https://wolfram.com/xid/0b8dsol2sb-ebm0xs" data-code="Files/RandomVariate.en/i_13.txt" ></div> <div id="593827692" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_14.png" data-in-width="214" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-j3t2ny" data-code="Files/RandomVariate.en/i_14.txt" ></div> <div id="149513476" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_15.png" data-in-width="391" data-in-height="58" data-link="https://wolfram.com/xid/0b8dsol2sb-cravme" data-code="Files/RandomVariate.en/i_15.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_9.png" data-out-width="226" data-out-height="141" ></div> </div> </div> <div> <h2 id="1293636265" class="toggle">Scope<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(22)</span></h2> <div class="hideable"> <div> <h3 id="134677597" class="toggle">Basic Uses<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(5)</span></h3> <div class="hideable"> <p><a name="180473455"></a>Use <span class="IF"><a href="/language/ref/RandomVariate.html">RandomVariate</a></span> to generate arrays of different sizes and dimensions:</p> <div id="232123645" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_16.png" data-in-width="193" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-d4hh1b" data-code="Files/RandomVariate.en/i_16.txt" ></div> <p><a name="114563848"></a>A vector:</p> <div id="103494993" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_17.png" data-in-width="154" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-bzwji7" data-code="Files/RandomVariate.en/i_17.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_10.png" data-out-width="100" data-out-height="18" ></div> <div id="276227813" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_18.png" data-in-width="94" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-euqs03" data-code="Files/RandomVariate.en/i_18.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_11.png" data-out-width="16" data-out-height="18" ></div> <p><a name="634016967"></a>A matrix:</p> <div id="15732259" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_19.png" data-in-width="169" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-jnhdh" data-code="Files/RandomVariate.en/i_19.txt" ></div> <div class="clipboard-output" data-out="Out[4]=" data-out-num="4" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_12.png" data-out-width="310" data-out-height="18" ></div> <div id="369346595" class="clipboard-input" data-in="In[5]:=" data-in-num="5" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_20.png" data-in-width="94" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-gd6nxx" data-code="Files/RandomVariate.en/i_20.txt" ></div> <div class="clipboard-output" data-out="Out[5]=" data-out-num="5" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_13.png" data-out-width="29" data-out-height="18" ></div> <p><a name="6877230"></a>A rank-3 tensor:</p> <div id="179157179" class="clipboard-input" data-in="In[6]:=" data-in-num="6" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_21.png" data-in-width="184" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-c8x8ul" data-code="Files/RandomVariate.en/i_21.txt" ></div> <div class="clipboard-output" data-out="Out[6]=" data-out-num="6" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_14.png" data-out-width="436" data-out-height="53" ></div> <div id="181411777" class="clipboard-input" data-in="In[7]:=" data-in-num="7" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_22.png" data-in-width="94" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-daakib" data-code="Files/RandomVariate.en/i_22.txt" ></div> <div class="clipboard-output" data-out="Out[7]=" data-out-num="7" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_15.png" data-out-width="42" data-out-height="18" ></div> <div class="ExLine"><a name="929189923"></a></div> <p><a name="165931632"></a>Generate high-precision random variates:</p> <div id="339932610" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_23.png" data-in-width="382" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-fwn7ys" data-code="Files/RandomVariate.en/i_23.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_16.png" data-out-width="148" data-out-height="18" ></div> <div id="55750567" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_24.png" data-in-width="389" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-7g7o5" data-code="Files/RandomVariate.en/i_24.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_17.png" data-out-width="542" data-out-height="35" ></div> <div class="ExLine"><a name="83523866"></a></div> <p><a name="653975753"></a>Use <span class="IF"><a href="/language/ref/SeedRandom.html">SeedRandom</a></span> to get repeatable random values:</p> <div id="113623371" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_25.png" data-in-width="355" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-b5xmm1" data-code="Files/RandomVariate.en/i_25.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_18.png" data-out-width="190" data-out-height="18" ></div> <div id="574177663" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_26.png" data-in-width="355" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-jr4wlt" data-code="Files/RandomVariate.en/i_26.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_19.png" data-out-width="190" data-out-height="18" ></div> <div class="ExLine"><a name="690269114"></a></div> <p><a name="29604057"></a>Generate random variates for a univariate continuous distribution:</p> <div id="18312902" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_27.png" data-in-width="249" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-k6sl0" data-code="Files/RandomVariate.en/i_27.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_20.png" data-out-width="44" data-out-height="18" ></div> <p><a name="16354281"></a>Discrete univariate distribution:</p> <div id="568510475" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_28.png" data-in-width="290" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-jorfrx" data-code="Files/RandomVariate.en/i_28.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_21.png" data-out-width="61" data-out-height="18" ></div> <p><a name="205488747"></a>Continuous multivariate distribution:</p> <div id="712571365" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_29.png" data-big="413 19" data-small="413 19" data-link="https://wolfram.com/xid/0b8dsol2sb-l2i5vb" data-code="Files/RandomVariate.en/i_29.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_22.png" data-out-width="246" data-out-height="18" ></div> <p><a name="16360043"></a>Discrete multivariate distribution:</p> <div id="4292067" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_30.png" data-big="413 19" data-small="413 19" data-link="https://wolfram.com/xid/0b8dsol2sb-ct92d" data-code="Files/RandomVariate.en/i_30.txt" ></div> <div class="clipboard-output" data-out="Out[4]=" data-out-num="4" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_23.png" data-out-width="311" data-out-height="18" ></div> <div class="ExLine"><a name="6406061"></a></div> <p><a name="128079327"></a>Generate random variates for a quantity distribution:</p> <div id="296865066" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_31.png" data-in-width="322" data-in-height="21" data-link="https://wolfram.com/xid/0b8dsol2sb-e604t4" data-code="Files/RandomVariate.en/i_31.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_24.png" data-out-width="66" data-out-height="18" ></div> <p><a name="45000996"></a>Generate array of variates:</p> <div id="130414685" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_32.png" data-in-width="351" data-in-height="21" data-link="https://wolfram.com/xid/0b8dsol2sb-cfxiwf" data-code="Files/RandomVariate.en/i_32.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_25.png" data-out-width="230" data-out-height="47" ></div> <p><a name="20326875"></a>Generate random vectors:</p> <div id="200995672" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_33.png" data-big="518 24" data-small="518 24" data-link="https://wolfram.com/xid/0b8dsol2sb-dlybje" data-code="Files/RandomVariate.en/i_33.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_26.png" data-out-width="304" data-out-height="55" ></div> </div> </div> <div> <h3 id="302064935" class="toggle">Parametric Distributions<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(4)</span></h3> <div class="hideable"> <p><a name="978436521"></a>Generate random variates for univariate continuous distributions:</p> <div id="68245520" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_34.png" data-in-width="239" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-bew0u6" data-code="Files/RandomVariate.en/i_34.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_27.png" data-out-width="50" data-out-height="18" ></div> <div id="132282174" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_35.png" data-in-width="302" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-cg1ju4" data-code="Files/RandomVariate.en/i_35.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_28.png" data-out-width="232" data-out-height="18" ></div> <div id="61438696" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_36.png" data-in-width="274" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-bau4oq" data-code="Files/RandomVariate.en/i_36.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_29.png" data-out-width="358" data-out-height="18" ></div> <div id="34542229" class="clipboard-input" data-in="In[5]:=" data-in-num="5" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_37.png" data-big="534 39" data-small="534 39" data-link="https://wolfram.com/xid/0b8dsol2sb-uum8n" data-code="Files/RandomVariate.en/i_37.txt" ></div> <div class="clipboard-output" data-out="Out[5]=" data-out-num="5" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_30.png" data-out-width="241" data-out-height="150" ></div> <div class="ExLine"><a name="135496617"></a></div> <p><a name="32001641"></a>Generate random variates for univariate discrete distributions:</p> <div id="227035570" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_38.png" data-in-width="288" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-d1gf1w" data-code="Files/RandomVariate.en/i_38.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_31.png" data-out-width="8" data-out-height="18" ></div> <div id="145170" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_39.png" data-in-width="353" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-deas" data-code="Files/RandomVariate.en/i_39.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_32.png" data-out-width="75" data-out-height="18" ></div> <div id="521577970" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_40.png" data-in-width="284" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-iwtie8" data-code="Files/RandomVariate.en/i_40.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_33.png" data-out-width="96" data-out-height="18" ></div> <div id="25169928" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_41.png" data-big="515 58" data-small="515 58" data-link="https://wolfram.com/xid/0b8dsol2sb-o9riy" data-code="Files/RandomVariate.en/i_41.txt" ></div> <div class="clipboard-output" data-out="Out[4]=" data-out-num="4" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_34.png" data-out-width="241" data-out-height="152" ></div> <div class="ExLine"><a name="818305952"></a></div> <p><a name="30195016"></a>Generate random variates for multivariate continuous distributions:</p> <div id="511051234" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_42.png" data-in-width="345" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-iqjvxw" data-code="Files/RandomVariate.en/i_42.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_35.png" data-out-width="100" data-out-height="18" ></div> <div id="308675363" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_43.png" data-big="503 39" data-small="503 39" data-link="https://wolfram.com/xid/0b8dsol2sb-fd19px" data-code="Files/RandomVariate.en/i_43.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_36.png" data-out-width="310" data-out-height="18" ></div> <div id="90992176" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_44.png" data-in-width="343" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-bsgkaq" data-code="Files/RandomVariate.en/i_44.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_37.png" data-out-width="541" data-out-height="35" ></div> <div id="465873457" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_45.png" data-big="516 58" data-small="516 58" data-link="https://wolfram.com/xid/0b8dsol2sb-hznkjn" data-code="Files/RandomVariate.en/i_45.txt" ></div> <div class="clipboard-output" data-out="Out[4]=" data-out-num="4" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_38.png" data-out-width="261" data-out-height="104" ></div> <div class="ExLine"><a name="320545537"></a></div> <p><a name="343785322"></a>Generate random variates for multivariate discrete distributions:</p> <div id="170587067" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_46.png" data-in-width="396" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-c3uj3x" data-code="Files/RandomVariate.en/i_46.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_39.png" data-out-width="42" data-out-height="18" ></div> <div id="149030418" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_47.png" data-in-width="391" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-cq0iv4" data-code="Files/RandomVariate.en/i_47.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_40.png" data-out-width="96" data-out-height="18" ></div> <div id="348695324" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_48.png" data-big="487 19" data-small="487 19" data-link="https://wolfram.com/xid/0b8dsol2sb-f1v1bi" data-code="Files/RandomVariate.en/i_48.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_41.png" data-out-width="376" data-out-height="18" ></div> <div id="600528341" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_49.png" data-big="502 78" data-small="502 78" data-link="https://wolfram.com/xid/0b8dsol2sb-j7tow3" data-code="Files/RandomVariate.en/i_49.txt" ></div> <div class="clipboard-output" data-out="Out[4]=" data-out-num="4" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_42.png" data-out-width="471" data-out-height="209" ></div> </div> </div> <div> <h3 id="16249985" class="toggle">Nonparametric Distributions<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(4)</span></h3> <div class="hideable"> <p><a name="412635079"></a>Generate random variates for a univariate <span class="IF"><a href="/language/ref/EmpiricalDistribution.html">EmpiricalDistribution</a></span>:</p> <div id="795776966" class="clipboard-input" data-in="In[6]:=" data-in-num="6" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_50.png" data-big="495 19" data-small="495 19" data-link="https://wolfram.com/xid/0b8dsol2sb-nf2jp0" data-code="Files/RandomVariate.en/i_50.txt" ></div> <div id="87646087" class="clipboard-input" data-in="In[8]:=" data-in-num="8" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_51.png" data-in-width="392" data-in-height="39" data-link="https://wolfram.com/xid/0b8dsol2sb-bqguft" data-code="Files/RandomVariate.en/i_51.txt" ></div> <div class="clipboard-output" data-out="Out[8]=" data-out-num="8" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_43.png" data-out-width="241" data-out-height="154" ></div> <p><a name="129987459"></a>Using a multivariate empirical distribution:</p> <div id="617434556" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_52.png" data-big="478 19" data-small="478 19" data-link="https://wolfram.com/xid/0b8dsol2sb-khv1t6" data-code="Files/RandomVariate.en/i_52.txt" ></div> <div id="72283987" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_53.png" data-in-width="134" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-bhbkyt" data-code="Files/RandomVariate.en/i_53.txt" ></div> <div class="clipboard-output" data-out="Out[4]=" data-out-num="4" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_44.png" data-out-width="365" data-out-height="18" ></div> <div class="ExLine"><a name="684249997"></a></div> <p><a name="160513536"></a>Using a univariate <span class="IF"><a href="/language/ref/HistogramDistribution.html">HistogramDistribution</a></span>:</p> <div id="143867672" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_54.png" data-big="502 19" data-small="502 19" data-link="https://wolfram.com/xid/0b8dsol2sb-cnxvai" data-code="Files/RandomVariate.en/i_54.txt" ></div> <div id="461926599" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_55.png" data-in-width="159" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-hxay4p" data-code="Files/RandomVariate.en/i_55.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_45.png" data-out-width="311" data-out-height="18" ></div> <p><a name="191515604"></a>A multivariate histogram distribution:</p> <div id="218527491" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_56.png" data-big="481 19" data-small="481 19" data-link="https://wolfram.com/xid/0b8dsol2sb-dwd26d" data-code="Files/RandomVariate.en/i_56.txt" ></div> <div id="464425005" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_57.png" data-big="458 19" data-small="458 19" data-link="https://wolfram.com/xid/0b8dsol2sb-hysiwv" data-code="Files/RandomVariate.en/i_57.txt" ></div> <div class="clipboard-output" data-out="Out[4]=" data-out-num="4" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_46.png" data-out-width="172" data-out-height="18" ></div> <div class="ExLine"><a name="65311157"></a></div> <p><a name="143426250"></a>Using a univariate <span class="IF"><a href="/language/ref/KernelMixtureDistribution.html">KernelMixtureDistribution</a></span>:</p> <div id="154771206" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_58.png" data-big="472 19" data-small="472 19" data-link="https://wolfram.com/xid/0b8dsol2sb-cufkig" data-code="Files/RandomVariate.en/i_58.txt" ></div> <div id="29297630" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_59.png" data-in-width="384" data-in-height="42" data-link="https://wolfram.com/xid/0b8dsol2sb-rp8hc" data-code="Files/RandomVariate.en/i_59.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_47.png" data-out-width="241" data-out-height="154" ></div> <div class="ExLine"><a name="236191483"></a></div> <p><a name="429738405"></a>Using censored data with <span class="IF"><a href="/language/ref/SurvivalDistribution.html">SurvivalDistribution</a></span>:</p> <div id="294262857" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_60.png" data-in-width="330" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-e5hcyj" data-code="Files/RandomVariate.en/i_60.txt" ></div> <div id="178261268" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_61.png" data-in-width="303" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-c8e1j6" data-code="Files/RandomVariate.en/i_61.txt" ></div> <div id="484093309" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_62.png" data-big="421 19" data-small="421 19" data-link="https://wolfram.com/xid/0b8dsol2sb-iah22n" data-code="Files/RandomVariate.en/i_62.txt" ></div> <div id="10905654" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_63.png" data-in-width="141" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-gr044" data-code="Files/RandomVariate.en/i_63.txt" ></div> <div class="clipboard-output" data-out="Out[4]=" data-out-num="4" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_48.png" data-out-width="248" data-out-height="18" ></div> </div> </div> <div> <h3 id="334445480" class="toggle">Derived Distributions<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(9)</span></h3> <div class="hideable"> <p><a name="61494149"></a>Generate random variates for a <span class="IF"><a href="/language/ref/TransformedDistribution.html">TransformedDistribution</a></span>:</p> <div id="446485828" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_64.png" data-big="473 58" data-small="473 58" data-link="https://wolfram.com/xid/0b8dsol2sb-hn30ye" data-code="Files/RandomVariate.en/i_64.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_49.png" data-out-width="337" data-out-height="53" ></div> <p><a name="69471516"></a>An equivalent way of generating the same random variates:</p> <div id="635798024" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_65.png" data-in-width="323" data-in-height="58" data-link="https://wolfram.com/xid/0b8dsol2sb-kstm6i" data-code="Files/RandomVariate.en/i_65.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_50.png" data-out-width="337" data-out-height="53" ></div> <div class="ExLine"><a name="9679608"></a></div> <p><a name="542381439"></a>Generate random variates for a <span class="IF"><a href="/language/ref/ProductDistribution.html">ProductDistribution</a></span>:</p> <div id="36874562" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_66.png" data-big="499 19" data-small="499 19" data-link="https://wolfram.com/xid/0b8dsol2sb-v8mvo" data-code="Files/RandomVariate.en/i_66.txt" ></div> <div id="333153708" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_67.png" data-in-width="239" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-fsmxby" data-code="Files/RandomVariate.en/i_67.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_51.png" data-out-width="487" data-out-height="18" ></div> <p><a name="183276415"></a>An equivalent way of generating the same random variates:</p> <div id="19957962" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_68.png" data-in-width="362" data-in-height="58" data-link="https://wolfram.com/xid/0b8dsol2sb-l51x4" data-code="Files/RandomVariate.en/i_68.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_52.png" data-out-width="487" data-out-height="18" ></div> <div class="ExLine"><a name="564724414"></a></div> <p><a name="16456733"></a>Using a component mixture of normal distributions:</p> <div id="181972816" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_69.png" data-big="525 19" data-small="525 19" data-link="https://wolfram.com/xid/0b8dsol2sb-damleq" data-code="Files/RandomVariate.en/i_69.txt" ></div> <div id="87271424" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_70.png" data-in-width="209" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-bp8tci" data-code="Files/RandomVariate.en/i_70.txt" ></div> <div id="399102666" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_71.png" data-in-width="393" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-gvwfvg" data-code="Files/RandomVariate.en/i_71.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_53.png" data-out-width="241" data-out-height="150" ></div> <div class="ExLine"><a name="154294262"></a></div> <p><a name="227816646"></a>Parameter mixture of exponential distributions:</p> <div id="62439589" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_72.png" data-big="411 39" data-small="411 39" data-link="https://wolfram.com/xid/0b8dsol2sb-bbgkzb" data-code="Files/RandomVariate.en/i_72.txt" ></div> <div id="6140481" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_73.png" data-in-width="204" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-dxwa7" data-code="Files/RandomVariate.en/i_73.txt" ></div> <p><a name="234018700"></a>Compare the variance of the sample with the variance of the distribution:</p> <div id="172767415" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_74.png" data-in-width="207" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-c45ag5" data-code="Files/RandomVariate.en/i_74.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_54.png" data-out-width="113" data-out-height="18" ></div> <div class="ExLine"><a name="100853472"></a></div> <p><a name="767378198"></a>Truncated normal distribution:</p> <div id="14038216" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_75.png" data-in-width="355" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-im58q" data-code="Files/RandomVariate.en/i_75.txt" ></div> <div id="378477776" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_76.png" data-in-width="204" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-gjmdlu" data-code="Files/RandomVariate.en/i_76.txt" ></div> <div id="218802939" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_77.png" data-in-width="378" data-in-height="39" data-link="https://wolfram.com/xid/0b8dsol2sb-dwjzpp" data-code="Files/RandomVariate.en/i_77.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_55.png" data-out-width="241" data-out-height="153" ></div> <div class="ExLine"><a name="182182055"></a></div> <p><a name="118024079"></a>Censored exponential distribution:</p> <div id="160255930" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_78.png" data-in-width="399" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-cxo4jw" data-code="Files/RandomVariate.en/i_78.txt" ></div> <div id="434486152" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_79.png" data-in-width="204" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-hgytx2" data-code="Files/RandomVariate.en/i_79.txt" ></div> <p><a name="701867978"></a>Compare the kurtosis for the sample with the kurtosis for the distribution:</p> <div id="81493536" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_80.png" data-in-width="202" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-bmsy3m" data-code="Files/RandomVariate.en/i_80.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_56.png" data-out-width="100" data-out-height="18" ></div> <div class="ExLine"><a name="154764768"></a></div> <p><a name="779934211"></a>Marginal distribution:</p> <div id="756902426" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_81.png" data-in-width="381" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-msxbxo" data-code="Files/RandomVariate.en/i_81.txt" ></div> <div id="53612817" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_82.png" data-in-width="204" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-57d67" data-code="Files/RandomVariate.en/i_82.txt" ></div> <p><a name="483393286"></a>Compute probabilities using the sample and the marginal distribution:</p> <div id="469350741" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_83.png" data-in-width="236" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-h1p3mv" data-code="Files/RandomVariate.en/i_83.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_57.png" data-out-width="44" data-out-height="18" ></div> <div id="547440308" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_84.png" data-in-width="207" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-jb7txi" data-code="Files/RandomVariate.en/i_84.txt" ></div> <div class="clipboard-output" data-out="Out[4]=" data-out-num="4" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_58.png" data-out-width="50" data-out-height="18" ></div> <div class="ExLine"><a name="93451802"></a></div> <p><a name="89055050"></a>Copula distribution:</p> <div id="141155118" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_85.png" data-in-width="399" data-in-height="39" data-link="https://wolfram.com/xid/0b8dsol2sb-cmbp9s" data-code="Files/RandomVariate.en/i_85.txt" ></div> <div id="31781093" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_86.png" data-in-width="204" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-s7gqf" data-code="Files/RandomVariate.en/i_86.txt" ></div> <p><a name="554640037"></a>Compare the value of a moment for the sample with that for the copula distribution:</p> <div id="44631915" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_87.png" data-in-width="129" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-0uwhp" data-code="Files/RandomVariate.en/i_87.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_59.png" data-out-width="44" data-out-height="18" ></div> <div id="245482125" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_88.png" data-in-width="114" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-ecfth7" data-code="Files/RandomVariate.en/i_88.txt" ></div> <div class="clipboard-output" data-out="Out[4]=" data-out-num="4" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_60.png" data-out-width="533" data-out-height="65" ></div> <div id="411632070" class="clipboard-input" data-in="In[5]:=" data-in-num="5" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_89.png" data-in-width="31" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-g3czmg" data-code="Files/RandomVariate.en/i_89.txt" ></div> <div class="clipboard-output" data-out="Out[5]=" data-out-num="5" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_61.png" data-out-width="50" data-out-height="18" ></div> <div class="ExLine"><a name="132538303"></a></div> <p><a name="31972139"></a>Formula distribution:</p> <div id="739070477" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_90.png" data-in-width="402" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-mia4pr" data-code="Files/RandomVariate.en/i_90.txt" ></div> <div id="75515871" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_91.png" data-in-width="204" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-bi8upd" data-code="Files/RandomVariate.en/i_91.txt" ></div> <div id="56643870" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_92.png" data-in-width="386" data-in-height="39" data-link="https://wolfram.com/xid/0b8dsol2sb-70cy4" data-code="Files/RandomVariate.en/i_92.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_62.png" data-out-width="241" data-out-height="156" ></div> </div> </div> </div> </div> <div> <h2 id="2061341341" class="toggle">Options<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(1)</span></h2> <div class="hideable"> <div> <h3 id="336924853" class="toggle">WorkingPrecision<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(1)</span></h3> <div class="hideable"> <p><a name="619123407"></a>By default <span class="IF"><a href="/language/ref/MachinePrecision.html">MachinePrecision</a></span> random numbers are generated for continuous distributions:</p> <div id="863372206" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_93.png" data-in-width="285" data-in-height="39" data-link="https://wolfram.com/xid/0b8dsol2sb-okbcjk" data-code="Files/RandomVariate.en/i_93.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_63.png" data-out-width="271" data-out-height="18" ></div> <div id="3976206" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_94.png" data-big="526 39" data-small="526 39" data-link="https://wolfram.com/xid/0b8dsol2sb-cnicg" data-code="Files/RandomVariate.en/i_94.txt" ></div> <div class="clipboard-output" data-out="Out[4]=" data-out-num="4" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_64.png" data-out-width="271" data-out-height="18" ></div> <p><a name="100376501"></a>Use the <span class="IF"><a href="/language/ref/WorkingPrecision.html">WorkingPrecision</a></span> option to generate numbers with arbitrary precision:</p> <div id="40498572" class="clipboard-input" data-in="In[5]:=" data-in-num="5" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_95.png" data-big="439 19" data-small="439 19" data-link="https://wolfram.com/xid/0b8dsol2sb-yea6m" data-code="Files/RandomVariate.en/i_95.txt" ></div> <div class="clipboard-output" data-out="Out[5]=" data-out-num="5" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_65.png" data-out-width="542" data-out-height="35" ></div> </div> </div> </div> </div> <div> <h2 id="258228157" class="toggle">Applications<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(30)</span></h2> <div class="hideable"> <div> <h3 id="45264" class="toggle">Pictures of Random Data<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(6)</span></h3> <div class="hideable"> <p><a name="947810264"></a>Generate random data for a continuous distribution and compare its histogram to the PDF:</p> <div id="3408444" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_96.png" data-in-width="341" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-cbb9a" data-code="Files/RandomVariate.en/i_96.txt" ></div> <div id="833393797" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_97.png" data-big="428 58" data-small="428 58" data-link="https://wolfram.com/xid/0b8dsol2sb-n2gs1z" data-code="Files/RandomVariate.en/i_97.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_66.png" data-out-width="241" data-out-height="150" ></div> <div class="ExLine"><a name="4377748"></a></div> <p><a name="693161436"></a>Generate random data for a discrete distribution and compare its histogram to the PDF:</p> <div id="42876276" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_98.png" data-in-width="369" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-zs9ty" data-code="Files/RandomVariate.en/i_98.txt" ></div> <div id="22133026" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_99.png" data-in-width="324" data-in-height="78" data-link="https://wolfram.com/xid/0b8dsol2sb-ngn8k" data-code="Files/RandomVariate.en/i_99.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_67.png" data-out-width="241" data-out-height="150" ></div> <div class="ExLine"><a name="7754075"></a></div> <p><a name="142603972"></a>Generate random data for a bivariate distribution and compare its histogram to the PDF:</p> <div id="446974309" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_100.png" data-big="440 19" data-small="440 19" data-link="https://wolfram.com/xid/0b8dsol2sb-hoehvb" data-code="Files/RandomVariate.en/i_100.txt" ></div> <div id="6330936" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_101.png" data-big="542 58" data-small="542 58" data-link="https://wolfram.com/xid/0b8dsol2sb-d1y9m" data-code="Files/RandomVariate.en/i_101.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_68.png" data-out-width="226" data-out-height="175" ></div> <div class="ExLine"><a name="609727920"></a></div> <p><a name="19984396"></a>Compare the plots of random data for continuous multivariate distributions:</p> <div id="54126742" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_102.png" data-big="535 117" data-small="535 117" data-link="https://wolfram.com/xid/0b8dsol2sb-6ieqw" data-code="Files/RandomVariate.en/i_102.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_69.png" data-out-width="478" data-out-height="188" ></div> <div class="ExLine"><a name="234387144"></a></div> <p><a name="224251027"></a>Consider vectors with standard normal components:</p> <div id="117706252" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_103.png" data-big="537 19" data-small="537 19" data-link="https://wolfram.com/xid/0b8dsol2sb-b8c40e" data-code="Files/RandomVariate.en/i_103.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_70.png" data-out-width="191" data-out-height="241" ></div> <p><a name="31388223"></a>The angle will follow a uniform distribution:</p> <div id="230579372" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_104.png" data-in-width="351" data-in-height="21" data-link="https://wolfram.com/xid/0b8dsol2sb-d3kegu" data-code="Files/RandomVariate.en/i_104.txt" ></div> <div id="442505845" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_105.png" data-big="466 39" data-small="466 39" data-link="https://wolfram.com/xid/0b8dsol2sb-hlqpzb" data-code="Files/RandomVariate.en/i_105.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_71.png" data-out-width="241" data-out-height="150" ></div> <p><a name="489962697"></a>The norm will follow a Rayleigh distribution:</p> <div id="123659208" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_106.png" data-big="412 39" data-small="412 39" data-link="https://wolfram.com/xid/0b8dsol2sb-cbwqca" data-code="Files/RandomVariate.en/i_106.txt" ></div> <div class="clipboard-output" data-out="Out[4]=" data-out-num="4" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_72.png" data-out-width="241" data-out-height="157" ></div> <div id="64140120" class="clipboard-input" data-in="In[5]:=" data-in-num="5" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_107.png" data-in-width="344" data-in-height="39" data-link="https://wolfram.com/xid/0b8dsol2sb-bcg04a" data-code="Files/RandomVariate.en/i_107.txt" ></div> <div class="clipboard-output" data-out="Out[5]=" data-out-num="5" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_73.png" data-out-width="126" data-out-height="18" ></div> <div class="ExLine"><a name="51338556"></a></div> <p><a name="311685749"></a>Consider three-dimensional vectors with standard normal components:</p> <div id="547897241" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_108.png" data-big="505 39" data-small="505 39" data-link="https://wolfram.com/xid/0b8dsol2sb-jchmh3" data-code="Files/RandomVariate.en/i_108.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_74.png" data-out-width="151" data-out-height="166" ></div> <p><a name="46278636"></a>The <span class="IM"><img src="Files/RandomVariate.en/1.png" height="15" width="7" alt="" /></span> angle in spherical coordinates follows a uniform distribution: </p> <div id="442220380" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_109.png" data-in-width="351" data-in-height="21" data-link="https://wolfram.com/xid/0b8dsol2sb-hlklpq" data-code="Files/RandomVariate.en/i_109.txt" ></div> <div id="491959294" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_110.png" data-big="524 58" data-small="524 58" data-link="https://wolfram.com/xid/0b8dsol2sb-ie6oh8" data-code="Files/RandomVariate.en/i_110.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_75.png" data-out-width="241" data-out-height="159" ></div> <p><a name="88191313"></a>The norm will follow a <span class="IM"><img src="Files/RandomVariate.en/2.png" height="15" width="10" alt="" /></span> distribution:</p> <div id="273430655" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_111.png" data-in-width="379" data-in-height="39" data-link="https://wolfram.com/xid/0b8dsol2sb-es2up9" data-code="Files/RandomVariate.en/i_111.txt" ></div> <div class="clipboard-output" data-out="Out[4]=" data-out-num="4" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_76.png" data-out-width="241" data-out-height="154" ></div> <div id="214660079" class="clipboard-input" data-in="In[5]:=" data-in-num="5" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_112.png" data-in-width="367" data-in-height="39" data-link="https://wolfram.com/xid/0b8dsol2sb-dt2619" data-code="Files/RandomVariate.en/i_112.txt" ></div> <div class="clipboard-output" data-out="Out[5]=" data-out-num="5" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_77.png" data-out-width="97" data-out-height="18" ></div> </div> </div> <div> <h3 id="35198578" class="toggle">Distribution Properties<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(5)</span></h3> <div class="hideable"> <p><a name="436025968"></a>Verify the Poisson approximation to the binomial distribution using random variates:</p> <div id="6203256" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_113.png" data-in-width="114" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-dy8qy" data-code="Files/RandomVariate.en/i_113.txt" ></div> <div id="38259538" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_114.png" data-in-width="337" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-w2bi8" data-code="Files/RandomVariate.en/i_114.txt" ></div> <div id="37438645" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_115.png" data-in-width="314" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-wkp4n" data-code="Files/RandomVariate.en/i_115.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_78.png" data-out-width="129" data-out-height="18" ></div> <div id="653468681" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_116.png" data-in-width="46" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-k3cdx3" data-code="Files/RandomVariate.en/i_116.txt" ></div> <div id="281702947" class="clipboard-input" data-in="In[5]:=" data-in-num="5" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_117.png" data-in-width="314" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-exz5n5" data-code="Files/RandomVariate.en/i_117.txt" ></div> <div id="691046323" class="clipboard-input" data-in="In[6]:=" data-in-num="6" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_118.png" data-in-width="314" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-lpps1h" data-code="Files/RandomVariate.en/i_118.txt" ></div> <div class="clipboard-output" data-out="Out[6]=" data-out-num="6" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_79.png" data-out-width="148" data-out-height="18" ></div> <div class="ExLine"><a name="112939171"></a></div> <p><a name="178205625"></a>Define a truncated triangular distribution:</p> <div id="18073833" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_119.png" data-big="408 19" data-small="408 19" data-link="https://wolfram.com/xid/0b8dsol2sb-k1n47" data-code="Files/RandomVariate.en/i_119.txt" ></div> <p><a name="45679485"></a>Generate random numbers from this distribution:</p> <div id="366845284" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_120.png" data-in-width="214" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-gco1w2" data-code="Files/RandomVariate.en/i_120.txt" ></div> <div id="28862333" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_121.png" data-big="418 78" data-small="418 78" data-link="https://wolfram.com/xid/0b8dsol2sb-rgwlr" data-code="Files/RandomVariate.en/i_121.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_80.png" data-out-width="241" data-out-height="154" ></div> <p><a name="776042759"></a>Mean, variance, and kurtosis:</p> <div id="7500930" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_122.png" data-in-width="173" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-eq11g" data-code="Files/RandomVariate.en/i_122.txt" ></div> <div class="clipboard-output" data-out="Out[4]=" data-out-num="4" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_81.png" data-out-width="100" data-out-height="18" ></div> <div id="55687513" class="clipboard-input" data-in="In[5]:=" data-in-num="5" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_123.png" data-in-width="213" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-7fu1n" data-code="Files/RandomVariate.en/i_123.txt" ></div> <div class="clipboard-output" data-out="Out[5]=" data-out-num="5" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_82.png" data-out-width="106" data-out-height="18" ></div> <div id="131839211" class="clipboard-input" data-in="In[6]:=" data-in-num="6" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_124.png" data-in-width="208" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-cgr12l" data-code="Files/RandomVariate.en/i_124.txt" ></div> <div class="clipboard-output" data-out="Out[6]=" data-out-num="6" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_83.png" data-out-width="100" data-out-height="18" ></div> <p><a name="330261502"></a>Moments:</p> <div id="207069651" class="clipboard-input" data-in="In[7]:=" data-in-num="7" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_125.png" data-in-width="238" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-dpkh81" data-code="Files/RandomVariate.en/i_125.txt" ></div> <div class="clipboard-output" data-out="Out[7]=" data-out-num="7" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_84.png" data-out-width="87" data-out-height="18" ></div> <div id="200766130" class="clipboard-input" data-in="In[8]:=" data-in-num="8" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_126.png" data-in-width="328" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-dltee8" data-code="Files/RandomVariate.en/i_126.txt" ></div> <div class="clipboard-output" data-out="Out[8]=" data-out-num="8" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_85.png" data-out-width="128" data-out-height="18" ></div> <p><a name="55020557"></a>Probabilities and expectations:</p> <div id="552923119" class="clipboard-input" data-in="In[9]:=" data-in-num="9" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_127.png" data-big="412 19" data-small="412 19" data-link="https://wolfram.com/xid/0b8dsol2sb-jfhcht" data-code="Files/RandomVariate.en/i_127.txt" ></div> <div class="clipboard-output" data-out="Out[9]=" data-out-num="9" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_86.png" data-out-width="113" data-out-height="18" ></div> <div id="57588720" class="clipboard-input" data-in="In[10]:=" data-in-num="10" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_128.png" data-in-width="381" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-8kl0y" data-code="Files/RandomVariate.en/i_128.txt" ></div> <div class="clipboard-output" data-out="Out[10]=" data-out-num="10" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_87.png" data-out-width="100" data-out-height="18" ></div> <div class="ExLine"><a name="357230828"></a></div> <p><a name="54915694"></a>Simulate the distribution of a function of a random variable:</p> <div id="835254812" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_129.png" data-big="425 19" data-small="425 19" data-link="https://wolfram.com/xid/0b8dsol2sb-n3ko0u" data-code="Files/RandomVariate.en/i_129.txt" ></div> <div id="421486460" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_130.png" data-in-width="191" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-g877bi" data-code="Files/RandomVariate.en/i_130.txt" ></div> <p><a name="155873863"></a>Compare the mean and variance of the sample with those for the distribution:</p> <div id="458891452" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_131.png" data-in-width="134" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-hvhw62" data-code="Files/RandomVariate.en/i_131.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_88.png" data-out-width="100" data-out-height="18" ></div> <div id="7179302" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_132.png" data-in-width="170" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-ej5vc" data-code="Files/RandomVariate.en/i_132.txt" ></div> <div class="clipboard-output" data-out="Out[4]=" data-out-num="4" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_89.png" data-out-width="35" data-out-height="18" ></div> <div class="ExLine"><a name="170953344"></a></div> <p><a name="82601253"></a>Generate random data from a normal distribution:</p> <div id="116684546" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_133.png" data-in-width="204" data-in-height="39" data-link="https://wolfram.com/xid/0b8dsol2sb-b7q8no" data-code="Files/RandomVariate.en/i_133.txt" ></div> <p><a name="642083772"></a>Define nonparametric distributions using this data:</p> <div id="276798663" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_134.png" data-in-width="271" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-eu21h1" data-code="Files/RandomVariate.en/i_134.txt" ></div> <div id="157265046" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_135.png" data-in-width="317" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-cvw0rs" data-code="Files/RandomVariate.en/i_135.txt" ></div> <div id="176345913" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_136.png" data-in-width="320" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-c69znv" data-code="Files/RandomVariate.en/i_136.txt" ></div> <div id="276716125" class="clipboard-input" data-in="In[5]:=" data-in-num="5" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_137.png" data-in-width="259" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-eu09tb" data-code="Files/RandomVariate.en/i_137.txt" ></div> <p><a name="261127405"></a>Compare the mean and variance of these distributions:</p> <div id="39147809" class="clipboard-input" data-in="In[6]:=" data-in-num="6" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_138.png" data-big="459 19" data-small="459 19" data-link="https://wolfram.com/xid/0b8dsol2sb-xlcxf" data-code="Files/RandomVariate.en/i_138.txt" ></div> <div class="clipboard-output" data-out="Out[6]=" data-out-num="6" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_90.png" data-out-width="210" data-out-height="18" ></div> <div id="152871066" class="clipboard-input" data-in="In[7]:=" data-in-num="7" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_139.png" data-big="479 19" data-small="479 19" data-link="https://wolfram.com/xid/0b8dsol2sb-ctaucs" data-code="Files/RandomVariate.en/i_139.txt" ></div> <div class="clipboard-output" data-out="Out[7]=" data-out-num="7" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_91.png" data-out-width="203" data-out-height="18" ></div> <div class="ExLine"><a name="2112865469"></a></div> <p><a name="140350691"></a>Estimate an unknown slice distribution of a random process:</p> <div id="937019231" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_140.png" data-in-width="178" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-pr5ux9" data-code="Files/RandomVariate.en/i_140.txt" ></div> <p><a name="984631966"></a>Slice distribution is unknown:</p> <div id="200468780" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_141.png" data-in-width="93" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-dlm0zi" data-code="Files/RandomVariate.en/i_141.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_92.png" data-out-width="181" data-out-height="18" ></div> <p><a name="218925721"></a>Generate a random sample of paths:</p> <div id="845105536" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_142.png" data-in-width="235" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-n9ftv2" data-code="Files/RandomVariate.en/i_142.txt" ></div> <p><a name="1236171733"></a>Visualize its probability density function:</p> <div id="1581515453" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_143.png" data-in-width="171" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-0fvne3" data-code="Files/RandomVariate.en/i_143.txt" ></div> <div class="clipboard-output" data-out="Out[4]=" data-out-num="4" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_93.png" data-out-width="241" data-out-height="154" ></div> <p><a name="637477478"></a>Test if it fits a standard normal distribution:</p> <div id="288057863" class="clipboard-input" data-in="In[5]:=" data-in-num="5" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_144.png" data-big="429 19" data-small="429 19" data-link="https://wolfram.com/xid/0b8dsol2sb-e1sc5l" data-code="Files/RandomVariate.en/i_144.txt" ></div> <div class="clipboard-output" data-out="Out[5]=" data-out-num="5" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_94.png" data-out-width="482" data-out-height="35" ></div> </div> </div> <div> <h3 id="89897879" class="toggle">Random Experiments<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(4)</span></h3> <div class="hideable"> <p><a name="425560764"></a>Simulate 10 throws of a fair six-sided die:</p> <div id="43796256" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_145.png" data-in-width="345" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-0czoy" data-code="Files/RandomVariate.en/i_145.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_95.png" data-out-width="132" data-out-height="18" ></div> <p><a name="373802"></a>Simulate seven throws of a pair of fair six-sided dice:</p> <div id="437840789" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_146.png" data-in-width="362" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-hiyqef" data-code="Files/RandomVariate.en/i_146.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_96.png" data-out-width="239" data-out-height="18" ></div> <div class="ExLine"><a name="10123513"></a></div> <p><a name="118719060"></a>A coin-tossing experiment consists of tossing a fair coin repeatedly until a head results. Simulate the process:</p> <div id="185990725" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_147.png" data-in-width="297" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-dc0pnb" data-code="Files/RandomVariate.en/i_147.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_97.png" data-out-width="132" data-out-height="18" ></div> <div id="671226255" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_148.png" data-big="448 19" data-small="448 19" data-link="https://wolfram.com/xid/0b8dsol2sb-ldwzr1" data-code="Files/RandomVariate.en/i_148.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_98.png" data-out-width="241" data-out-height="159" ></div> <div class="ExLine"><a name="86751188"></a></div> <p><a name="108968625"></a>A radioactive material on average emits 3.2 <span class="IM"><img src="Files/RandomVariate.en/3.png" height="15" width="9" alt="" /></span>-particles per second; show the distribution. Simulate a typical particle-count experiment for 10 minutes: </p> <div id="689352201" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_149.png" data-in-width="386" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-lophuj" data-code="Files/RandomVariate.en/i_149.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_99.png" data-out-width="241" data-out-height="156" ></div> <div class="ExLine"><a name="35972582"></a></div> <p><a name="629314278"></a>Simulate a symmetric random walk with values <span class="IF">-1</span> and <span class="IF">1</span>:</p> <div id="544374480" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_150.png" data-big="476 39" data-small="476 39" data-link="https://wolfram.com/xid/0b8dsol2sb-jad4bm" data-code="Files/RandomVariate.en/i_150.txt" ></div> <div id="132760585" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_151.png" data-in-width="262" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-chbs0b" data-code="Files/RandomVariate.en/i_151.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_100.png" data-out-width="241" data-out-height="143" ></div> </div> </div> <div> <h3 id="457488237" class="toggle">Estimation and Hypothesis Testing<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(3)</span></h3> <div class="hideable"> <p><a name="133570865"></a>Generate random data for a normal distribution:</p> <div id="415623582" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_152.png" data-in-width="341" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-g5qjhs" data-code="Files/RandomVariate.en/i_152.txt" ></div> <p><a name="24270754"></a>Estimate the distribution parameters using the random data:</p> <div id="211709173" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_153.png" data-in-width="370" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-dsbx4n" data-code="Files/RandomVariate.en/i_153.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_101.png" data-out-width="144" data-out-height="18" ></div> <div class="ExLine"><a name="80175384"></a></div> <p><a name="240046475"></a>Generate high-precision random data for a component mixture distribution:</p> <div id="1666335" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_154.png" data-big="499 39" data-small="499 39" data-link="https://wolfram.com/xid/0b8dsol2sb-9z1d" data-code="Files/RandomVariate.en/i_154.txt" ></div> <p><a name="734759230"></a>Estimate the mixture probabilities, assuming the component distributions are known:</p> <div id="497720428" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_155.png" data-big="520 39" data-small="520 39" data-link="https://wolfram.com/xid/0b8dsol2sb-iil5tq" data-code="Files/RandomVariate.en/i_155.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_102.png" data-out-width="407" data-out-height="52" ></div> <div class="ExLine"><a name="305451850"></a></div> <p><a name="151132681"></a>Given a binormal sample, the <span class="IM"><img src="Files/RandomVariate.en/4.png" height="15" width="8" alt="" /></span>-statistic follows a shifted <span class="IF"><a href="/language/ref/FisherZDistribution.html">FisherZDistribution</a></span>:</p> <div id="283224497" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_156.png" data-in-width="393" data-in-height="39" data-link="https://wolfram.com/xid/0b8dsol2sb-eywrpf" data-code="Files/RandomVariate.en/i_156.txt" ></div> <p><a name="41436556"></a>Generate the distribution of <span class="IM"><img src="Files/RandomVariate.en/5.png" height="15" width="8" alt="" /></span>-statistics for binormal samples of size <span class="IM"><img src="Files/RandomVariate.en/6.png" height="15" width="8" alt="" /></span>:</p> <div id="656728058" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_157.png" data-big="542 19" data-small="542 19" data-link="https://wolfram.com/xid/0b8dsol2sb-k498wc" data-code="Files/RandomVariate.en/i_157.txt" ></div> <p><a name="86473177"></a>Visually compare the <span class="IM"><img src="Files/RandomVariate.en/7.png" height="15" width="8" alt="" /></span>-statistic distribution to a shifted <span class="IF"><a href="/language/ref/FisherZDistribution.html">FisherZDistribution</a></span>:</p> <div id="111897414" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_158.png" data-big="529 19" data-small="529 19" data-link="https://wolfram.com/xid/0b8dsol2sb-b4wmvs" data-code="Files/RandomVariate.en/i_158.txt" ></div> <div id="826884372" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_159.png" data-big="457 39" data-small="457 39" data-link="https://wolfram.com/xid/0b8dsol2sb-nylacm" data-code="Files/RandomVariate.en/i_159.txt" ></div> <div class="clipboard-output" data-out="Out[4]=" data-out-num="4" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_103.png" data-out-width="241" data-out-height="154" ></div> <p><a name="37396173"></a><span class="IF"><a href="/language/ref/DistributionFitTest.html">DistributionFitTest</a></span> confirms the result:</p> <div id="378067778" class="clipboard-input" data-in="In[5]:=" data-in-num="5" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_160.png" data-big="433 19" data-small="433 19" data-link="https://wolfram.com/xid/0b8dsol2sb-gjdk80" data-code="Files/RandomVariate.en/i_160.txt" ></div> <div class="clipboard-output" data-out="Out[5]=" data-out-num="5" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_104.png" data-out-width="50" data-out-height="18" ></div> </div> </div> <div> <h3 id="179694420" class="toggle">Quality<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(3)</span></h3> <div class="hideable"> <p><a name="1227062034"></a>Suppose there are 5 defective items in a batch of 10 items, and 6 items are selected for testing. Simulate the number of defective items found:</p> <div id="552696469" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_161.png" data-in-width="355" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-jfchlz" data-code="Files/RandomVariate.en/i_161.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_105.png" data-out-width="260" data-out-height="18" ></div> <div id="363448400" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_162.png" data-in-width="157" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-gan8u6" data-code="Files/RandomVariate.en/i_162.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_106.png" data-out-width="241" data-out-height="161" ></div> <div class="ExLine"><a name="50109494"></a></div> <p><a name="177048023"></a>Out of 10 bulbs produced, one is defective. Simulate the production of 100 bulbs:</p> <div id="639862953" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_163.png" data-in-width="352" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-ku8ro7" data-code="Files/RandomVariate.en/i_163.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_107.png" data-out-width="447" data-out-height="53" ></div> <p><a name="6542522"></a>Find the percentage of good bulbs:</p> <div id="261538955" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_164.png" data-in-width="96" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-elzy09" data-code="Files/RandomVariate.en/i_164.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_108.png" data-out-width="14" data-out-height="18" ></div> <p><a name="151449864"></a>Find the average number of good bulbs per batch of 100:</p> <div id="214138112" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_165.png" data-in-width="236" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-dtr0a6" data-code="Files/RandomVariate.en/i_165.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_109.png" data-out-width="14" data-out-height="18" ></div> <p><a name="299530973"></a>Find the probability that a randomly selected bulb is good:</p> <div id="588217138" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_166.png" data-in-width="313" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-j0hti8" data-code="Files/RandomVariate.en/i_166.txt" ></div> <div class="clipboard-output" data-out="Out[4]=" data-out-num="4" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_110.png" data-out-width="18" data-out-height="30" ></div> <div class="ExLine"><a name="734060179"></a></div> <p><a name="12294983"></a>A shipment of products is inspected in batches of 60 and each batch is inspected up to rejection when the 10<img src="Files/RandomVariate.en/8.png" height="19" width="11" style="vertical-align:middle;" alt="^(th)" title="^(th)" /> defective item is found. What is the probability of a batch being rejected if 20% of the items are defective?</p> <div id="851884555" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_167.png" data-big="431 19" data-small="431 19" data-link="https://wolfram.com/xid/0b8dsol2sb-odg4l5" data-code="Files/RandomVariate.en/i_167.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_111.png" data-out-width="50" data-out-height="18" ></div> <p><a name="13355946"></a>Alternatively, compute the same result by truncating the distribution:</p> <div id="85027" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_168.png" data-big="470 39" data-small="470 39" data-link="https://wolfram.com/xid/0b8dsol2sb-b3v5" data-code="Files/RandomVariate.en/i_168.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_112.png" data-out-width="50" data-out-height="18" ></div> <p><a name="20484749"></a>Simulate the number of non-defective products in rejected batches:</p> <div id="195593130" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_169.png" data-big="459 19" data-small="459 19" data-link="https://wolfram.com/xid/0b8dsol2sb-diqiws" data-code="Files/RandomVariate.en/i_169.txt" ></div> <div id="333458294" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_170.png" data-in-width="200" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-fstgco" data-code="Files/RandomVariate.en/i_170.txt" ></div> <div class="clipboard-output" data-out="Out[4]=" data-out-num="4" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_113.png" data-out-width="389" data-out-height="18" ></div> <p><a name="147121381"></a>Illustrate the ratio in each batch:</p> <div id="500557896" class="clipboard-input" data-in="In[5]:=" data-in-num="5" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_171.png" data-big="438 19" data-small="438 19" data-link="https://wolfram.com/xid/0b8dsol2sb-ikay8a" data-code="Files/RandomVariate.en/i_171.txt" ></div> <div class="clipboard-output" data-out="Out[5]=" data-out-num="5" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_114.png" data-out-width="241" data-out-height="150" ></div> <p><a name="161534868"></a>Find the average ratio of non-defective to defective products in rejected batches:</p> <div id="67191799" class="clipboard-input" data-in="In[6]:=" data-in-num="6" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_172.png" data-in-width="226" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-beafs5" data-code="Files/RandomVariate.en/i_172.txt" ></div> <div class="clipboard-output" data-out="Out[6]=" data-out-num="6" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_115.png" data-out-width="44" data-out-height="18" ></div> </div> </div> <div> <h3 id="84735122" class="toggle">Traffic<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(3)</span></h3> <div class="hideable"> <p><a name="99023702"></a>The number of customers arriving at a service desk follows <span class="IF"><a href="/language/ref/PoissonDistribution.html">PoissonDistribution</a></span> with mean 0.6, and the number of customers already in line before the service desk opens follows <span class="IF"><a href="/language/ref/PoissonDistribution.html">PoissonDistribution</a></span> with mean 5. The number of customers served until there is no one in line follows <span class="IF"><a href="/language/ref/PoissonConsulDistribution.html">PoissonConsulDistribution</a></span>:</p> <div id="21138893" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_173.png" data-in-width="249" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-mvc5r" data-code="Files/RandomVariate.en/i_173.txt" ></div> <p><a name="55324307"></a>Plot the probability mass function:</p> <div id="627498198" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_174.png" data-in-width="220" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-knvqzs" data-code="Files/RandomVariate.en/i_174.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_116.png" data-out-width="241" data-out-height="151" ></div> <p><a name="2573785"></a>Simulate numbers of customers served at 30 busy periods:</p> <div id="175110" class="clipboard-input" data-in="In[6]:=" data-in-num="6" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_175.png" data-big="432 39" data-small="432 39" data-link="https://wolfram.com/xid/0b8dsol2sb-d1eg" data-code="Files/RandomVariate.en/i_175.txt" ></div> <div class="clipboard-output" data-out="Out[6]=" data-out-num="6" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_117.png" data-out-width="241" data-out-height="155" ></div> <div class="ExLine"><a name="11103288"></a></div> <p><a name="184114943"></a>The average number of accidents in a city is 100 per day. Simulate the daily accidents:</p> <div id="474811808" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_176.png" data-in-width="281" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-h4y5e6" data-code="Files/RandomVariate.en/i_176.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_118.png" data-out-width="377" data-out-height="35" ></div> <div id="696732908" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_177.png" data-in-width="157" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-ls3ot6" data-code="Files/RandomVariate.en/i_177.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_119.png" data-out-width="241" data-out-height="152" ></div> <div class="ExLine"><a name="540790764"></a></div> <p><a name="942321105"></a>The expected number of raindrops falling into a bucket in a five-second interval is 20. Simulate the raindrop count for each five-second interval:</p> <div id="256963718" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_178.png" data-in-width="274" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-ei9wrc" data-code="Files/RandomVariate.en/i_178.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_120.png" data-out-width="389" data-out-height="18" ></div> <div id="27022017" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_179.png" data-in-width="157" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-qdglv" data-code="Files/RandomVariate.en/i_179.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_121.png" data-out-width="241" data-out-height="155" ></div> </div> </div> <div> <h3 id="376219746" class="toggle">Finance<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(1)</span></h3> <div class="hideable"> <p><a name="1418658"></a>Assuming daily logarithmic return of the stock market follows a stable distribution, simulate and visualize stock prices over a period of 5 years:</p> <div id="198675917" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_180.png" data-big="500 39" data-small="500 39" data-link="https://wolfram.com/xid/0b8dsol2sb-dkkllr" data-code="Files/RandomVariate.en/i_180.txt" ></div> <div id="64904069" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_181.png" data-in-width="310" data-in-height="39" data-link="https://wolfram.com/xid/0b8dsol2sb-bcxek3" data-code="Files/RandomVariate.en/i_181.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_122.png" data-out-width="241" data-out-height="148" ></div> </div> </div> <div> <h3 id="739346558" class="toggle">Other Applications<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(5)</span></h3> <div class="hideable"> <p><a name="246704609"></a><span class="IF"><a href="/language/ref/RandomVariate.html">RandomVariate</a></span> can generate complex numbers if necessary:</p> <div id="589873617" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_182.png" data-big="529 19" data-small="529 19" data-link="https://wolfram.com/xid/0b8dsol2sb-j1hboj" data-code="Files/RandomVariate.en/i_182.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_123.png" data-out-width="123" data-out-height="18" ></div> <div class="ExLine"><a name="6242780"></a></div> <p><a name="118033183"></a>Evaluate an integral numerically using a Monte Carlo scheme:</p> <div id="1844722966" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_183.png" data-in-width="136" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-4sk3mw" data-code="Files/RandomVariate.en/i_183.txt" ></div> <p><a name="953297598"></a>Approximate with an interpolating function defined with uniformly distributed random nodes:</p> <div id="455077475" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_184.png" data-in-width="302" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-hs76a9" data-code="Files/RandomVariate.en/i_184.txt" ></div> <div id="1037477823" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_185.png" data-in-width="336" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-rfy1ap" data-code="Files/RandomVariate.en/i_185.txt" ></div> <p><a name="490323941"></a>Interpolate between the nodes:</p> <div id="388734205" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_186.png" data-in-width="151" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-gpp7in" data-code="Files/RandomVariate.en/i_186.txt" ></div> <div class="clipboard-output" data-out="Out[4]=" data-out-num="4" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_124.png" data-out-width="269" data-out-height="47" ></div> <div id="340467595" class="clipboard-input" data-in="In[5]:=" data-in-num="5" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_187.png" data-big="421 19" data-small="421 19" data-link="https://wolfram.com/xid/0b8dsol2sb-fwzorh" data-code="Files/RandomVariate.en/i_187.txt" ></div> <div class="clipboard-output" data-out="Out[5]=" data-out-num="5" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_125.png" data-out-width="226" data-out-height="138" ></div> <p><a name="1444784787"></a>Find the value of the integral using the interpolating function:</p> <div id="9989105" class="clipboard-input" data-in="In[6]:=" data-in-num="6" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_188.png" data-in-width="161" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-f8dxf" data-code="Files/RandomVariate.en/i_188.txt" ></div> <div class="clipboard-output" data-out="Out[6]=" data-out-num="6" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_126.png" data-out-width="44" data-out-height="18" ></div> <p><a name="644486733"></a>Compare with the value obtained using the original function:</p> <div id="344277980" class="clipboard-input" data-in="In[7]:=" data-in-num="7" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_189.png" data-in-width="145" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-fy9cvi" data-code="Files/RandomVariate.en/i_189.txt" ></div> <div class="clipboard-output" data-out="Out[7]=" data-out-num="7" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_127.png" data-out-width="266" data-out-height="30" ></div> <div id="148889902" class="clipboard-input" data-in="In[8]:=" data-in-num="8" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_190.png" data-in-width="31" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-cqxigw" data-code="Files/RandomVariate.en/i_190.txt" ></div> <div class="clipboard-output" data-out="Out[8]=" data-out-num="8" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_128.png" data-out-width="44" data-out-height="18" ></div> <div class="ExLine"><a name="114423753"></a></div> <p><a name="101649078"></a>Sample a Gaussian symmetric matrix:</p> <div id="4774452" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_191.png" data-big="415 19" data-small="415 19" data-link="https://wolfram.com/xid/0b8dsol2sb-c4l9y" data-code="Files/RandomVariate.en/i_191.txt" ></div> <p><a name="37641809"></a>Fit <span class="IF"><a href="/language/ref/WignerSemicircleDistribution.html">WignerSemicircleDistribution</a></span> to its eigenvalues:</p> <div id="30624332" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_192.png" data-big="488 19" data-small="488 19" data-link="https://wolfram.com/xid/0b8dsol2sb-sin56" data-code="Files/RandomVariate.en/i_192.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_129.png" data-out-width="210" data-out-height="18" ></div> <p><a name="717632094"></a>Compare the histogram of the eigenvalues with the PDF:</p> <div id="700472055" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_193.png" data-big="444 39" data-small="444 39" data-link="https://wolfram.com/xid/0b8dsol2sb-lvbtzd" data-code="Files/RandomVariate.en/i_193.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_130.png" data-out-width="241" data-out-height="145" ></div> <div class="ExLine"><a name="142241153"></a></div> <p><a name="32090272"></a>The heights of females in the United States follow normal distribution with mean 64 inches and standard deviation of 2 inches, while the heights of males in the United States follow normal distribution with mean 70 inches and standard deviation of 2 inches. If the population ratio of males to females is 1:1, then the heights of the whole population have the following bimodal distribution:</p> <div id="67655556" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_194.png" data-in-width="381" data-in-height="39" data-link="https://wolfram.com/xid/0b8dsol2sb-bekdna" data-code="Files/RandomVariate.en/i_194.txt" ></div> <div id="104392353" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_195.png" data-in-width="292" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-b0frxv" data-code="Files/RandomVariate.en/i_195.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_131.png" data-out-width="241" data-out-height="146" ></div> <p><a name="251192681"></a>Simulate the typical distribution of heights in a town of population 100:</p> <div id="17486478" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_196.png" data-in-width="331" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-ko2xs" data-code="Files/RandomVariate.en/i_196.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_132.png" data-out-width="241" data-out-height="156" ></div> <p><a name="28829182"></a>Find the probability that a person is at least 73 inches tall:</p> <div id="123772768" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_197.png" data-in-width="199" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-cby5yq" data-code="Files/RandomVariate.en/i_197.txt" ></div> <div class="clipboard-output" data-out="Out[4]=" data-out-num="4" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_133.png" data-out-width="56" data-out-height="18" ></div> <div class="ExLine"><a name="291361980"></a></div> <p><a name="142325060"></a>A basketball player shoots free throws until he hits 4 of them. His probability of scoring in any one of them is 0.7. Simulate the process:</p> <div id="93764591" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_198.png" data-in-width="374" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-bt3zh9" data-code="Files/RandomVariate.en/i_198.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_134.png" data-out-width="370" data-out-height="35" ></div> <div id="73302528" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_199.png" data-in-width="157" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-bhxevm" data-code="Files/RandomVariate.en/i_199.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_135.png" data-out-width="241" data-out-height="161" ></div> <p><a name="746022570"></a>Find the number of shots the player is expected to shoot:</p> <div id="899356450" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_200.png" data-in-width="369" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-o5ql5w" data-code="Files/RandomVariate.en/i_200.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_136.png" data-out-width="44" data-out-height="18" ></div> </div> </div> </div> </div> <div> <h2 id="2123667759" class="toggle">Properties & Relations<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(17)</span></h2> <div class="hideable"> <p><a name="977959341"></a><span class="IF"><a href="/language/ref/RandomInteger.html">RandomInteger</a></span> generates uniform discrete random variates: </p> <div id="242936506" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_201.png" data-in-width="169" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-eaw9ak" data-code="Files/RandomVariate.en/i_201.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_137.png" data-out-width="138" data-out-height="18" ></div> <div class="ExLine"><a name="309325584"></a></div> <p><a name="15633074"></a><span class="IF"><a href="/language/ref/RandomReal.html">RandomReal</a></span> generates uniform continuous variates: </p> <div id="77078790" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_202.png" data-in-width="151" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-bj6cns" data-code="Files/RandomVariate.en/i_202.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_138.png" data-out-width="487" data-out-height="18" ></div> <div class="ExLine"><a name="319023402"></a></div> <p><a name="853900778"></a><span class="IF"><a href="/language/ref/RandomChoice.html">RandomChoice</a></span> generates random choices with replacement from a list: </p> <div id="301925027" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_203.png" data-in-width="188" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-e91k4l" data-code="Files/RandomVariate.en/i_203.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_139.png" data-out-width="145" data-out-height="18" ></div> <div class="ExLine"><a name="20740371"></a></div> <p><a name="433400057"></a><span class="IF"><a href="/language/ref/RandomSample.html">RandomSample</a></span> generates random choice without replacement from a list: </p> <div id="29892019" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_204.png" data-in-width="193" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-r2y35" data-code="Files/RandomVariate.en/i_204.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_140.png" data-out-width="157" data-out-height="18" ></div> <div class="ExLine"><a name="584976172"></a></div> <p><a name="121033432"></a><span class="IF"><a href="/language/ref/RandomPrime.html">RandomPrime</a></span> generates a random prime number: </p> <div id="244640978" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_205.png" data-in-width="168" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-ebxsg0" data-code="Files/RandomVariate.en/i_205.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_141.png" data-out-width="183" data-out-height="18" ></div> <div class="ExLine"><a name="154339667"></a></div> <p><a name="355090246"></a><span class="IF"><a href="/language/ref/RandomImage.html">RandomImage</a></span> generates a random image: </p> <div id="189061317" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_206.png" data-in-width="326" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-deuixj" data-code="Files/RandomVariate.en/i_206.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_142.png" data-out-width="101" data-out-height="101" ></div> <div class="ExLine"><a name="132715836"></a></div> <p><a name="567262415"></a><span class="IF"><a href="/language/ref/RandomGraph.html">RandomGraph</a></span> generates a random graph: </p> <div id="174907123" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_207.png" data-in-width="349" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-c6e5hh" data-code="Files/RandomVariate.en/i_207.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_143.png" data-out-width="101" data-out-height="87" ></div> <div class="ExLine"><a name="265931263"></a></div> <p><a name="48175895"></a><span class="IF"><a href="/language/ref/RandomFunction.html">RandomFunction</a></span> generates a path for a random process:</p> <div id="7133197" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_208.png" data-in-width="163" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-ei6an" data-code="Files/RandomVariate.en/i_208.txt" ></div> <div id="193291760" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_209.png" data-in-width="283" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-dhc65u" data-code="Files/RandomVariate.en/i_209.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_144.png" data-out-width="241" data-out-height="147" ></div> <p><a name="905243064"></a>Use <span class="IF"><a href="/language/ref/RandomVariate.html">RandomVariate</a></span> to generate a sample for a time slice of the process:</p> <div id="395981046" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_210.png" data-in-width="218" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-gt1i7s" data-code="Files/RandomVariate.en/i_210.txt" ></div> <div id="323340666" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_211.png" data-in-width="304" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-fmsljg" data-code="Files/RandomVariate.en/i_211.txt" ></div> <div class="clipboard-output" data-out="Out[4]=" data-out-num="4" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_145.png" data-out-width="241" data-out-height="150" ></div> <div class="ExLine"><a name="569286366"></a></div> <p><a name="120600069"></a>Test whether the mean or median is zero by using <span class="IF"><a href="/language/ref/LocationTest.html">LocationTest</a></span>: </p> <div id="111198841" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_212.png" data-in-width="341" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-b4hnuz" data-code="Files/RandomVariate.en/i_212.txt" ></div> <div id="101280400" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_213.png" data-in-width="278" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-byk2qq" data-code="Files/RandomVariate.en/i_213.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_146.png" data-out-width="153" data-out-height="38" ></div> <p><a name="116519136"></a>Compare means or medians for several datasets using <span class="IF"><a href="/language/ref/LocationEquivalenceTest.html">LocationEquivalenceTest</a></span>: </p> <div id="83700561" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_214.png" data-in-width="350" data-in-height="58" data-link="https://wolfram.com/xid/0b8dsol2sb-bn391v" data-code="Files/RandomVariate.en/i_214.txt" ></div> <div id="40375428" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_215.png" data-big="441 19" data-small="441 19" data-link="https://wolfram.com/xid/0b8dsol2sb-ybn5y" data-code="Files/RandomVariate.en/i_215.txt" ></div> <div class="clipboard-output" data-out="Out[4]=" data-out-num="4" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_147.png" data-out-width="167" data-out-height="38" ></div> <div class="ExLine"><a name="633135918"></a></div> <p><a name="364275856"></a>Test whether two datasets have the same variance by using <span class="IF"><a href="/language/ref/VarianceTest.html">VarianceTest</a></span>: </p> <div id="108546307" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_216.png" data-in-width="335" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-b2ws5h" data-code="Files/RandomVariate.en/i_216.txt" ></div> <div id="113567091" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_217.png" data-in-width="334" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-b5we7p" data-code="Files/RandomVariate.en/i_217.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_148.png" data-out-width="178" data-out-height="77" ></div> <p><a name="123525071"></a>Test whether several datasets have the same variance by using <span class="IF"><a href="/language/ref/VarianceEquivalenceTest.html">VarianceEquivalenceTest</a></span>:</p> <div id="17647844" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_218.png" data-in-width="334" data-in-height="21" data-link="https://wolfram.com/xid/0b8dsol2sb-ksjf6" data-code="Files/RandomVariate.en/i_218.txt" ></div> <div id="53962229" class="clipboard-input" data-in="In[4]:=" data-in-num="4" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_219.png" data-in-width="337" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-6evs3" data-code="Files/RandomVariate.en/i_219.txt" ></div> <div class="clipboard-output" data-out="Out[4]=" data-out-num="4" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_149.png" data-out-width="164" data-out-height="64" ></div> <div class="ExLine"><a name="64923418"></a></div> <p><a name="144255930"></a>Use <span class="IF"><a href="/language/ref/DistributionFitTest.html">DistributionFitTest</a></span> to test goodness of fit between random data and a distribution: </p> <div id="611158005" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_220.png" data-in-width="343" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-kd5itj" data-code="Files/RandomVariate.en/i_220.txt" ></div> <div id="276119281" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_221.png" data-big="459 19" data-small="459 19" data-link="https://wolfram.com/xid/0b8dsol2sb-euohab" data-code="Files/RandomVariate.en/i_221.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_150.png" data-out-width="199" data-out-height="98" ></div> <div class="ExLine"><a name="31526185"></a></div> <p><a name="8882499"></a>Estimate distribution parameters from random data using <span class="IF"><a href="/language/ref/EstimatedDistribution.html">EstimatedDistribution</a></span>:</p> <div id="80527167" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_222.png" data-in-width="343" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-bl79f1" data-code="Files/RandomVariate.en/i_222.txt" ></div> <div id="119622782" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_223.png" data-in-width="375" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-b9h7tc" data-code="Files/RandomVariate.en/i_223.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_151.png" data-out-width="206" data-out-height="18" ></div> <div id="323922673" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_224.png" data-big="472 58" data-small="472 58" data-link="https://wolfram.com/xid/0b8dsol2sb-fm42mb" data-code="Files/RandomVariate.en/i_224.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_152.png" data-out-width="241" data-out-height="150" ></div> <div class="ExLine"><a name="3232664"></a></div> <p><a name="418195045"></a>Estimate nonparametric distributions from random data:</p> <div id="48329772" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_225.png" data-in-width="310" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-215ry" data-code="Files/RandomVariate.en/i_225.txt" ></div> <div id="291087641" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_226.png" data-big="430 39" data-small="430 39" data-link="https://wolfram.com/xid/0b8dsol2sb-e3lax3" data-code="Files/RandomVariate.en/i_226.txt" ></div> <div id="768366378" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_227.png" data-big="466 58" data-small="466 58" data-link="https://wolfram.com/xid/0b8dsol2sb-mzq1ks" data-code="Files/RandomVariate.en/i_227.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_153.png" data-out-width="478" data-out-height="122" ></div> <div class="ExLine"><a name="207186206"></a></div> <p><a name="39408439"></a>Compare random data to distributions using statistical visualization functions:</p> <div id="596677179" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_228.png" data-in-width="355" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-j5i5cd" data-code="Files/RandomVariate.en/i_228.txt" ></div> <div id="394863450" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_229.png" data-in-width="322" data-in-height="39" data-link="https://wolfram.com/xid/0b8dsol2sb-gtdkvg" data-code="Files/RandomVariate.en/i_229.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_154.png" data-out-width="261" data-out-height="81" ></div> <div class="ExLine"><a name="411624176"></a></div> <p><a name="395075744"></a>Compare multiple distributions using statistical charts:</p> <div id="107897593" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_230.png" data-big="457 19" data-small="457 19" data-link="https://wolfram.com/xid/0b8dsol2sb-b2iwln" data-code="Files/RandomVariate.en/i_230.txt" ></div> <div id="7839695" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_231.png" data-in-width="307" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-eybfl" data-code="Files/RandomVariate.en/i_231.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_155.png" data-out-width="261" data-out-height="72" ></div> <div class="ExLine"><a name="367997899"></a></div> <p><a name="620340652"></a>Plot histograms from random data:</p> <div id="193401886" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_232.png" data-in-width="404" data-in-height="39" data-link="https://wolfram.com/xid/0b8dsol2sb-dhfj4w" data-code="Files/RandomVariate.en/i_232.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_156.png" data-out-width="291" data-out-height="141" ></div> <div class="ExLine"><a name="341980267"></a></div> <p><a name="13617318"></a>Plot smooth kernel density estimates from data:</p> <div id="391524134" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_233.png" data-big="505 39" data-small="505 39" data-link="https://wolfram.com/xid/0b8dsol2sb-grdz8o" data-code="Files/RandomVariate.en/i_233.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_157.png" data-out-width="291" data-out-height="134" ></div> </div> </div> <div> <h2 id="1305812373" class="toggle">Possible Issues<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(3)</span></h2> <div class="hideable"> <p><a name="617729371"></a>The speed of random variate generation may depend on the distribution:</p> <div id="66266067" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/I_234.png" data-in-width="171" data-in-height="19" data-link="https://wolfram.com/xid/0b8dsol2sb-bdqlid" data-code="Files/RandomVariate.en/i_234.txt" ></div> <div id="340702069" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_235.png" data-big="453 39" data-small="453 39" data-link="https://wolfram.com/xid/0b8dsol2sb-fw4pon" data-code="Files/RandomVariate.en/i_235.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_158.png" data-out-width="168" data-out-height="18" ></div> <div class="ExLine"><a name="432016926"></a></div> <p><a name="82400264"></a>The <span class="IF"><a href="/language/ref/WorkingPrecision.html">WorkingPrecision</a></span> option is ignored for discrete distributions:</p> <div id="385420096" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_236.png" data-big="409 19" data-small="409 19" data-link="https://wolfram.com/xid/0b8dsol2sb-gnq6b2" data-code="Files/RandomVariate.en/i_236.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_159.png" data-out-width="67" data-out-height="18" ></div> <div class="ExLine"><a name="306359977"></a></div> <p><a name="42314440"></a>The result from <span class="IF"><a href="/language/ref/RandomVariate.html">RandomVariate</a></span> may include infinite quantities:</p> <div id="118494345" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_237.png" data-big="471 39" data-small="471 39" data-link="https://wolfram.com/xid/0b8dsol2sb-b8t03v" data-code="Files/RandomVariate.en/i_237.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_160.png" data-out-width="540" data-out-height="71" ></div> <p><a name="374144795"></a>Using a different level of precision avoids the problem in this case:</p> <div id="18785022" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src-swap="Files/RandomVariate.en/I_238.png" data-big="471 39" data-small="471 39" data-link="https://wolfram.com/xid/0b8dsol2sb-lgwwg" data-code="Files/RandomVariate.en/i_238.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/RandomVariate.en/O_161.png" data-out-width="431" data-out-height="88" ></div> </div> </div> <div class="clear"></div> </div></section><section id="SeeAlso" class="related-links"><div class="inner"> <h1>See Also</h1> <p class="inlineFunctionList"><span class="IF"><a href="/language/ref/SeedRandom.html">SeedRandom</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/BlockRandom.html">BlockRandom</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/RandomChoice.html">RandomChoice</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/RandomInteger.html">RandomInteger</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/RandomReal.html">RandomReal</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/RandomComplex.html">RandomComplex</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/RandomPoint.html">RandomPoint</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/RandomGeoPosition.html">RandomGeoPosition</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/RandomFunction.html">RandomFunction</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/RandomGraph.html">RandomGraph</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/RandomImage.html">RandomImage</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/RandomInstance.html">RandomInstance</a></span></p> <p class="inlineFunctionList"> <span class="sub-ref-heading">Function Repository: </span> <span class="IF"><a href="https://resources.wolframcloud.com/FunctionRepository/resources/MetropolisHastingsSequence"><span class="SeeAlsoRelated">MetropolisHastingsSequence</span></a></span> </p> </div></section><section id="RelatedGuides" class="related-links"><div class="inner"> <h1>Related Guides</h1> <ul class="functionList"> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/guide/RandomVariables.html">Random Variables</a> </li> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/guide/RandomNumberGeneration.html">Random Number Generation</a> </li> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/guide/ProbabilityAndStatistics.html">Probability & Statistics</a> </li> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/guide/MatrixDistributions.html">Matrix Distributions</a> </li> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/guide/MatricesAndLinearAlgebra.html">Matrices and Linear Algebra</a> </li> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/guide/ProbabilityWithQuantities.html">Probability & Statistics with Quantities</a> </li> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/guide/ScientificModels.html">Scientific Models</a> </li> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/guide/Statistics.html">Statistical Data Analysis</a> </li> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/guide/RandomGraphs.html">Random Graphs</a> </li> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/guide/Reliability.html">Reliability</a> </li> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/guide/ActuarialComputation.html">Actuarial Computation</a> </li> </ul> </div></section><section id="History" class="related-links"><div class="inner"> <h1>History</h1> <p class="inlineFunctionList"> <span class="history-text"><a href="/language/guide/SummaryOfNewFeaturesIn80">Introduced in 2010 <span class="history-version">(8.0)</span></a></span> </p> </div></section><section id="Citations" class="citations"><div class="inner"> <div class="citation"> <span class="citation-tooltip"><button type="button" class="citation-tooltip-button"><span class="citation-text">Cite this as:</span></button><span class="citation-default clipboard-inlineblock clipboard-hover">Wolfram Research (2010), RandomVariate, Wolfram Language function, https://reference.wolfram.com/language/ref/RandomVariate.html.</span><span class="citation-tooltip-content"><button class="x-close-svg"><img src="/language-assets/img/CitationCloseButton.svg" height="10px" width="10px" /></button><h4>Text</h4><p class="clipboard-inlineblock clipboard-hover">Wolfram Research (2010), RandomVariate, Wolfram Language function, https://reference.wolfram.com/language/ref/RandomVariate.html.</p><h4>CMS</h4><p class="clipboard-inlineblock clipboard-hover">Wolfram Language. 2010. "RandomVariate." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RandomVariate.html.</p><h4>APA</h4><p class="clipboard-inlineblock clipboard-hover">Wolfram Language. (2010). RandomVariate. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RandomVariate.html</p><h4>BibTeX</h4><p class="clipboard-inlineblock clipboard-hover citation-timestamp">@misc{reference.wolfram_2025_randomvariate, author="Wolfram Research", title="{RandomVariate}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/RandomVariate.html}", note=[Accessed: 17-February-2025 ]}</p><h4>BibLaTeX</h4><p class="clipboard-inlineblock clipboard-hover citation-timestamp">@online{reference.wolfram_2025_randomvariate, organization={Wolfram Research}, title={RandomVariate}, year={2010}, url={https://reference.wolfram.com/language/ref/RandomVariate.html}, note=[Accessed: 17-February-2025 ]}</p></span><span class="citation-overlay"></span></span> </div> </div></section> </div> <section class="feedback-wrapper"> <div class="inner"> <div class="feedback-content"> <button class="feedback"><span class="give">Give</span> Feedback</button><a class="toplink" href="#top"><span 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