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href="/w/index.php?title=%D8%AE%D8%A7%D8%B5:%D8%AF%D8%A7%D8%AE%D9%84_%DB%81%D9%88%DA%BA&returnto=%D8%AF%D9%88+%D8%B1%D9%82%D9%85%DB%8C+%D8%AA%D9%88%D8%B2%DB%8C%D8%B9" title="کھاتے میں داخل ہونے کی سفارش کی جاتی ہے؛ تاہم یہ ضروری نہیں [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>داخل ہوں</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pages for logged out editors <a href="/wiki/%D9%85%D8%B9%D8%A7%D9%88%D9%86%D8%AA:%D8%AA%D8%B9%D8%A7%D8%B1%D9%81" aria-label="ترمیم کاری کے متعلق مزید تفصیلات"><span>مزید تفصیلات</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%D8%AE%D8%A7%D8%B5:%D9%85%DB%8C%D8%B1%DB%8C_%D8%B4%D8%B1%D8%A7%DA%A9%D8%AA%DB%8C%DA%BA" title="اس آئی پی پتے سے انجام دی جانے والی تمام ترامیم کی فہرست [y]" accesskey="y"><span>شراکتیں</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%D8%AE%D8%A7%D8%B5:%D9%85%DB%8C%D8%B1%D8%A7_%D8%AA%D8%A8%D8%A7%D8%AF%D9%84%DB%81_%D8%AE%DB%8C%D8%A7%D9%84" title="اس آئی پی پتے کی ترامیم سے متعلق گفتگو [n]" accesskey="n"><span>تبادلۂ خیال</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="ویب گاہ"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="مندرجات" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">مندرجات</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">بغلی پٹی پر جائیں</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">چھپائیں</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">دیباچہ</div> </a> </li> <li id="toc-متوقع_قدر" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#متوقع_قدر"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>متوقع قدر</span> </div> </a> <ul id="toc-متوقع_قدر-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-تفاوت" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#تفاوت"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>تفاوت</span> </div> </a> <ul id="toc-تفاوت-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-مزید_دیکھیے" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#مزید_دیکھیے"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>مزید دیکھیے</span> </div> </a> <ul id="toc-مزید_دیکھیے-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="مندرجات" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="فہرست عناوین دیکھیں" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">فہرست عناوین دیکھیں</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">دو رقمی توزیع</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 52 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-52" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">52 زبانیں</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D9%88%D8%B2%D9%8A%D8%B9_%D8%AB%D9%86%D8%A7%D8%A6%D9%8A_%D8%A7%D9%84%D8%AD%D8%AF%D9%8A%D9%86" title="توزيع ثنائي الحدين – عربی" lang="ar" hreflang="ar" data-title="توزيع ثنائي الحدين" data-language-autonym="العربية" data-language-local-name="عربی" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D9%88%D8%B2%DB%8C%D8%B9_%D8%AF%D9%88%D8%AC%D9%85%D9%84%D9%87%E2%80%8C%D8%A7%DB%8C" title="توزیع دوجمله‌ای – فارسی" lang="fa" hreflang="fa" data-title="توزیع دوجمله‌ای" data-language-autonym="فارسی" data-language-local-name="فارسی" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Binomial_distribution" title="Binomial distribution – انگریزی" lang="en" hreflang="en" data-title="Binomial distribution" data-language-autonym="English" data-language-local-name="انگریزی" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Distribuci%C3%B3n_bin%C3%B3mica" title="Distribución binómica – اسٹوریائی" lang="ast" hreflang="ast" data-title="Distribución binómica" data-language-autonym="Asturianu" data-language-local-name="اسٹوریائی" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%A6%E0%A7%8D%E0%A6%AC%E0%A6%BF%E0%A6%AA%E0%A6%A6%E0%A7%80_%E0%A6%AC%E0%A6%A8%E0%A7%8D%E0%A6%9F%E0%A6%A8" title="দ্বিপদী বন্টন – بنگلہ" lang="bn" hreflang="bn" data-title="দ্বিপদী বন্টন" data-language-autonym="বাংলা" data-language-local-name="بنگلہ" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%91%D1%96%D0%BD%D0%BE%D0%BC%D0%BD%D0%B0%D0%B5_%D1%80%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%D0%BA%D0%B0%D0%B2%D0%B0%D0%BD%D0%BD%D0%B5" title="Біномнае размеркаванне – بیلاروسی" lang="be" hreflang="be" data-title="Біномнае размеркаванне" data-language-autonym="Беларуская" data-language-local-name="بیلاروسی" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Distribuci%C3%B3_binomial" title="Distribució binomial – کیٹالان" lang="ca" hreflang="ca" data-title="Distribució binomial" data-language-autonym="Català" data-language-local-name="کیٹالان" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Binomick%C3%A9_rozd%C4%9Blen%C3%AD" title="Binomické rozdělení – چیک" lang="cs" hreflang="cs" data-title="Binomické rozdělení" data-language-autonym="Čeština" data-language-local-name="چیک" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Binomialfordelingen" title="Binomialfordelingen – ڈینش" lang="da" hreflang="da" data-title="Binomialfordelingen" data-language-autonym="Dansk" data-language-local-name="ڈینش" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Binomialverteilung" title="Binomialverteilung – جرمن" lang="de" hreflang="de" data-title="Binomialverteilung" data-language-autonym="Deutsch" data-language-local-name="جرمن" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Binoomjaotus" title="Binoomjaotus – اسٹونین" lang="et" hreflang="et" data-title="Binoomjaotus" data-language-autonym="Eesti" data-language-local-name="اسٹونین" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%94%CE%B9%CF%89%CE%BD%CF%85%CE%BC%CE%B9%CE%BA%CE%AE_%CE%BA%CE%B1%CF%84%CE%B1%CE%BD%CE%BF%CE%BC%CE%AE" title="Διωνυμική κατανομή – یونانی" lang="el" hreflang="el" data-title="Διωνυμική κατανομή" data-language-autonym="Ελληνικά" data-language-local-name="یونانی" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Distribuci%C3%B3n_binomial" title="Distribución binomial – ہسپانوی" lang="es" hreflang="es" data-title="Distribución binomial" data-language-autonym="Español" data-language-local-name="ہسپانوی" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Banaketa_binomial" title="Banaketa binomial – باسکی" lang="eu" hreflang="eu" data-title="Banaketa binomial" data-language-autonym="Euskara" data-language-local-name="باسکی" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fr badge-Q17437798 badge-goodarticle mw-list-item" title="بہترین مضمون"><a href="https://fr.wikipedia.org/wiki/Loi_binomiale" title="Loi binomiale – فرانسیسی" lang="fr" hreflang="fr" data-title="Loi binomiale" data-language-autonym="Français" data-language-local-name="فرانسیسی" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Distribuci%C3%B3n_binomial" title="Distribución binomial – گالیشیائی" lang="gl" hreflang="gl" data-title="Distribución binomial" data-language-autonym="Galego" data-language-local-name="گالیشیائی" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9D%B4%ED%95%AD_%EB%B6%84%ED%8F%AC" title="이항 분포 – کوریائی" lang="ko" hreflang="ko" data-title="이항 분포" data-language-autonym="한국어" data-language-local-name="کوریائی" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%A6%E0%A5%8D%E0%A4%B5%E0%A4%BF%E0%A4%AA%E0%A4%A6_%E0%A4%B5%E0%A4%BF%E0%A4%A4%E0%A4%B0%E0%A4%A3" title="द्विपद वितरण – ہندی" lang="hi" hreflang="hi" data-title="द्विपद वितरण" data-language-autonym="हिन्दी" data-language-local-name="ہندی" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Distribusi_binomial" title="Distribusi binomial – انڈونیثیائی" lang="id" hreflang="id" data-title="Distribusi binomial" data-language-autonym="Bahasa Indonesia" data-language-local-name="انڈونیثیائی" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Distribuzione_binomiale" title="Distribuzione binomiale – اطالوی" lang="it" hreflang="it" data-title="Distribuzione binomiale" data-language-autonym="Italiano" data-language-local-name="اطالوی" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%91%D7%99%D7%A0%D7%95%D7%9E%D7%99%D7%AA" title="התפלגות בינומית – عبرانی" lang="he" hreflang="he" data-title="התפלגות בינומית" data-language-autonym="עברית" data-language-local-name="عبرانی" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%91%D0%B8%D0%BD%D0%BE%D0%BC%D0%B4%D1%8B%D2%9B_%D2%AF%D0%BB%D0%B5%D1%81%D1%82%D1%96%D1%80%D1%96%D0%BB%D1%83" title="Биномдық үлестірілу – قزاخ" lang="kk" hreflang="kk" data-title="Биномдық үлестірілу" data-language-autonym="Қазақша" data-language-local-name="قزاخ" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Binomi%C4%81lais_sadal%C4%ABjums" title="Binomiālais sadalījums – لیٹوین" lang="lv" hreflang="lv" data-title="Binomiālais sadalījums" data-language-autonym="Latviešu" data-language-local-name="لیٹوین" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Binominis_skirstinys" title="Binominis skirstinys – لیتھوینین" lang="lt" hreflang="lt" data-title="Binominis skirstinys" data-language-autonym="Lietuvių" data-language-local-name="لیتھوینین" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Binomi%C3%A1lis_eloszl%C3%A1s" title="Binomiális eloszlás – ہنگیرین" lang="hu" hreflang="hu" data-title="Binomiális eloszlás" data-language-autonym="Magyar" data-language-local-name="ہنگیرین" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%91%D0%B8%D0%BD%D0%BE%D0%BC%D0%BD%D0%B0_%D1%80%D0%B0%D1%81%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D0%B1%D0%B0" title="Биномна распределба – مقدونیائی" lang="mk" hreflang="mk" data-title="Биномна распределба" data-language-autonym="Македонски" data-language-local-name="مقدونیائی" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Taburan_binomial" title="Taburan binomial – مالے" lang="ms" hreflang="ms" data-title="Taburan binomial" data-language-autonym="Bahasa Melayu" data-language-local-name="مالے" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Binomiale_verdeling" title="Binomiale verdeling – ڈچ" lang="nl" hreflang="nl" data-title="Binomiale verdeling" data-language-autonym="Nederlands" data-language-local-name="ڈچ" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E4%BA%8C%E9%A0%85%E5%88%86%E5%B8%83" title="二項分布 – جاپانی" lang="ja" hreflang="ja" data-title="二項分布" data-language-autonym="日本語" data-language-local-name="جاپانی" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Binomisk_fordeling" title="Binomisk fordeling – نارویجین بوکمل" lang="nb" hreflang="nb" data-title="Binomisk fordeling" data-language-autonym="Norsk bokmål" data-language-local-name="نارویجین بوکمل" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Binomisk_fordeling" title="Binomisk fordeling – نارویجین نینورسک" lang="nn" hreflang="nn" data-title="Binomisk fordeling" data-language-autonym="Norsk nynorsk" data-language-local-name="نارویجین نینورسک" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Binomial_taqsimot" title="Binomial taqsimot – ازبیک" lang="uz" hreflang="uz" data-title="Binomial taqsimot" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="ازبیک" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Rozk%C5%82ad_dwumianowy" title="Rozkład dwumianowy – پولش" lang="pl" hreflang="pl" data-title="Rozkład dwumianowy" data-language-autonym="Polski" data-language-local-name="پولش" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Distribui%C3%A7%C3%A3o_binomial" title="Distribuição binomial – پُرتگالی" lang="pt" hreflang="pt" data-title="Distribuição binomial" data-language-autonym="Português" data-language-local-name="پُرتگالی" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Distribu%C8%9Bia_binomial%C4%83" title="Distribuția binomială – رومینین" lang="ro" hreflang="ro" data-title="Distribuția binomială" data-language-autonym="Română" data-language-local-name="رومینین" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%91%D0%B8%D0%BD%D0%BE%D0%BC%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%D0%B5_%D1%80%D0%B0%D1%81%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D0%B5%D0%BD%D0%B8%D0%B5" title="Биномиальное распределение – روسی" lang="ru" hreflang="ru" data-title="Биномиальное распределение" data-language-autonym="Русский" data-language-local-name="روسی" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Shp%C3%ABrndarja_binomiale" title="Shpërndarja binomiale – البانی" lang="sq" hreflang="sq" data-title="Shpërndarja binomiale" data-language-autonym="Shqip" data-language-local-name="البانی" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Binomial_distribution" title="Binomial distribution – Simple English" lang="en-simple" hreflang="en-simple" data-title="Binomial distribution" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Binomick%C3%A9_rozdelenie" title="Binomické rozdelenie – سلوواک" lang="sk" hreflang="sk" data-title="Binomické rozdelenie" data-language-autonym="Slovenčina" data-language-local-name="سلوواک" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Binomska_porazdelitev" title="Binomska porazdelitev – سلووینیائی" lang="sl" hreflang="sl" data-title="Binomska porazdelitev" data-language-autonym="Slovenščina" data-language-local-name="سلووینیائی" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Binomna_raspodela" title="Binomna raspodela – سربین" lang="sr" hreflang="sr" data-title="Binomna raspodela" data-language-autonym="Српски / srpski" data-language-local-name="سربین" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Sebaran_binomial" title="Sebaran binomial – سنڈانیز" lang="su" hreflang="su" data-title="Sebaran binomial" data-language-autonym="Sunda" data-language-local-name="سنڈانیز" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Binomijakauma" title="Binomijakauma – فینیش" lang="fi" hreflang="fi" data-title="Binomijakauma" data-language-autonym="Suomi" data-language-local-name="فینیش" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Binomialf%C3%B6rdelning" title="Binomialfördelning – سویڈش" lang="sv" hreflang="sv" data-title="Binomialfördelning" data-language-autonym="Svenska" data-language-local-name="سویڈش" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Distribusyong_binomial" title="Distribusyong binomial – ٹیگا لوگ" lang="tl" hreflang="tl" data-title="Distribusyong binomial" data-language-autonym="Tagalog" data-language-local-name="ٹیگا لوگ" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%88%E0%AE%B0%E0%AF%81%E0%AE%B1%E0%AF%81%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AF%81%E0%AE%AA%E0%AF%8D_%E0%AE%AA%E0%AE%B0%E0%AE%B5%E0%AE%B2%E0%AF%8D" title="ஈருறுப்புப் பரவல் – تمل" lang="ta" hreflang="ta" data-title="ஈருறுப்புப் பரவல்" data-language-autonym="தமிழ்" data-language-local-name="تمل" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B9%81%E0%B8%88%E0%B8%81%E0%B9%81%E0%B8%88%E0%B8%87%E0%B8%97%E0%B8%A7%E0%B8%B4%E0%B8%99%E0%B8%B2%E0%B8%A1" title="การแจกแจงทวินาม – تھائی" lang="th" hreflang="th" data-title="การแจกแจงทวินาม" data-language-autonym="ไทย" data-language-local-name="تھائی" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Binom_da%C4%9F%C4%B1l%C4%B1m%C4%B1" title="Binom dağılımı – ترکی" lang="tr" hreflang="tr" data-title="Binom dağılımı" data-language-autonym="Türkçe" data-language-local-name="ترکی" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%91%D1%96%D0%BD%D0%BE%D0%BC%D1%96%D0%B0%D0%BB%D1%8C%D0%BD%D0%B8%D0%B9_%D1%80%D0%BE%D0%B7%D0%BF%D0%BE%D0%B4%D1%96%D0%BB" title="Біноміальний розподіл – یوکرینیائی" lang="uk" hreflang="uk" data-title="Біноміальний розподіл" data-language-autonym="Українська" data-language-local-name="یوکرینیائی" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Ph%C3%A2n_ph%E1%BB%91i_nh%E1%BB%8B_th%E1%BB%A9c" title="Phân phối nhị thức – ویتنامی" lang="vi" hreflang="vi" data-title="Phân phối nhị thức" data-language-autonym="Tiếng Việt" data-language-local-name="ویتنامی" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E4%BA%8C%E9%A0%85%E5%88%86%E4%BD%88" title="二項分佈 – کینٹونیز" lang="yue" hreflang="yue" data-title="二項分佈" data-language-autonym="粵語" data-language-local-name="کینٹونیز" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%BA%8C%E9%A0%85%E5%BC%8F%E5%88%86%E5%B8%83" title="二項式分布 – چینی" lang="zh" hreflang="zh" data-title="二項式分布" data-language-autonym="中文" data-language-local-name="چینی" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q185547#sitelinks-wikipedia" title="ترمیم بین اللسانی روابط" class="wbc-editpage">ترمیم روابط</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="فضائے نام"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a 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class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">بغلی پٹی پر جائیں</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">چھپائیں</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">آزاد دائرۃ المعارف، ویکیپیڈیا سے</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-rtl mw-parser-output" lang="ur" dir="rtl"><table class="mw-collapsible mw-expanded wikitable" style="float:left; clear:left; margin:0 1em 0.4em 0em;"> <tbody><tr> <th>اصطلاح </th> <th>term </th></tr> <tr> <td> <p>اقدار <br /> توزیع <br /> تفاعل <br /> کمیت <br /> تَراكُمی <br /> دو رقمی <br /> متوقع قدر <br /> تَفاوُت </p> </td> <td style="text-align:left; font-family:arial; direction:LTR;"> <p>values <br /> distribution <br /> function <br /> mass <br /> cumulative <br /> binomial <br /> expected value <br /> variance </p> </td></tr></tbody></table> <figure typeof="mw:Error mw:File/Thumb"><a href="/w/index.php?title=%D8%AE%D8%A7%D8%B5:%D8%A7%D9%BE%D9%84%D9%88%DA%88&wpDestFile=Binomial_distribution_pmf.png" class="new" title="فائل:Binomial distribution pmf.png"><span class="mw-file-element mw-broken-media" data-width="280">فائل:Binomial distribution pmf.png</span></a><figcaption>تصویر 2: دو رقمی توزیع کی <i>احتمال کمیت تفاعل</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ p_{X}(.)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mo>.</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ p_{X}(.)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/235c66d7785c1c250050889475e3131b872c5326" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.226ex; height:2.843ex;" alt="{\displaystyle \ p_{X}(.)}"></span></figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/%D9%81%D8%A7%D8%A6%D9%84:Binomial_distribution_cdf.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/Binomial_distribution_cdf.png/280px-Binomial_distribution_cdf.png" decoding="async" width="280" height="210" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/Binomial_distribution_cdf.png/420px-Binomial_distribution_cdf.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/56/Binomial_distribution_cdf.png/560px-Binomial_distribution_cdf.png 2x" data-file-width="561" data-file-height="420" /></a><figcaption>تصویر 3: دو رقمی توزیع کی <i>تَراكُمی توزیع احتمال تفاعل</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ F_{X}(.)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mo>.</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ F_{X}(.)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ed4be71dd975c20fc44bb270c0c7a07637ba97b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.551ex; height:2.843ex;" alt="{\displaystyle \ F_{X}(.)}"></span></figcaption></figure> <p><i>دو رقمی توزیعِ احتمال</i> ایک <a href="/wiki/%D8%AA%D9%82%D8%B3%DB%8C%D9%85_%D8%A7%D8%AD%D8%AA%D9%85%D8%A7%D9%84" title="تقسیم احتمال">توزیعِ احتمال</a> ہے جو درج ذیل حالات میں کام آتی ہے۔ بعض اوقات ایک ہی تجربہ کو متعدد بار دہرایا جاتا ہے (جیسے سکے کو بار بار فضا میں اچھالا جائے)۔ ایسے بار بار آزمائش میں فرض کرو کہ: </p> <ul><li>دو ممکنہ نتائج ہیں، "کامیابی" اور "ناکامی"</li> <li>ہر آزمائش پر "کامیابی" کا احتمال <i>p</i> ہے اور "ناکامی" کا احتمال <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ 1-p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mn>1</mn> <mo>−</mo> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ 1-p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/237ce1b78f4fbddf0475ad53620f35ce473b68c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.753ex; height:2.509ex;" alt="{\displaystyle \ 1-p}"></span></li> <li>آزمائش کی تعداد <i>n</i> ہے</li> <li>ہر آزمائش دوسری آزمائشوں سے <a href="/wiki/%D8%A2%D8%B2%D8%A7%D8%AF_%D9%88%D8%A7%D9%82%D8%B9%D8%A7%D8%AA" class="mw-redirect" title="آزاد واقعات">آزاد</a> ہے</li></ul> <p>فرض کرو کہ تصادفی متغیر <i>X</i> ہے، جو ان <i>n</i> آزمائشوں میں "کامیابی" کی تعداد ظاہر کرتا ہے۔ اس متفرد تصادفی متغیر کا حیطہ </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \{0,1,2,\cdots ,n\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <mi>n</mi> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{0,1,2,\cdots ,n\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92f06ab2737ad7b28de87b3448b095c5216e852e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.453ex; height:2.843ex;" alt="{\displaystyle \{0,1,2,\cdots ,n\}}"></span></dd></dl> <p>ہے اور توزیعِ احتمال کمیت فنکشن </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ p_{X}(x)=\Pr(X=x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo movablelimits="true" form="prefix">Pr</mo> <mo stretchy="false">(</mo> <mi>X</mi> <mo>=</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ p_{X}(x)=\Pr(X=x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77b005f7c30935745d0bad1b66041c0c9fff67fe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.332ex; height:2.843ex;" alt="{\displaystyle \ p_{X}(x)=\Pr(X=x)}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{X}(x)={\frac {n!}{x!(n-x)!}}p^{x}(1-p)^{n-x}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mo>!</mo> </mrow> <mrow> <mi>x</mi> <mo>!</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mfrac> </mrow> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>p</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mi>x</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{X}(x)={\frac {n!}{x!(n-x)!}}p^{x}(1-p)^{n-x}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ae75d54e25762c11d2dd4545b500db4fbb0dbe3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; margin-left: -0.089ex; width:32.723ex; height:6.176ex;" alt="{\displaystyle p_{X}(x)={\frac {n!}{x!(n-x)!}}p^{x}(1-p)^{n-x}}"></span></dd></dl> <p>اس توزیع احتمال کو "دو رقمی توزیع" کے نام سے پکارا جاتا ہے۔ ( یہاں <i>!</i> کی علامت <a href="/wiki/%D8%B9%D8%A7%D9%85%D9%84%DB%8C%DB%81" title="عاملیہ">عامِلیہ</a> کو ظاہر کرتی ہے۔) </p> <div class="mw-heading mw-heading3"><h3 id="متوقع_قدر"><span id=".D9.85.D8.AA.D9.88.D9.82.D8.B9_.D9.82.D8.AF.D8.B1"></span>متوقع قدر</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%AF%D9%88_%D8%B1%D9%82%D9%85%DB%8C_%D8%AA%D9%88%D8%B2%DB%8C%D8%B9&action=edit&section=1" title="تدوینِ قطعہ: متوقع قدر"><span>ترمیم</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>دو رقمی توزیعِ احتمال شدہ تصادفی متغیر <i>X</i> کی <a href="/wiki/%D9%85%D8%AA%D9%88%D9%82%D8%B9_%D9%82%D8%AF%D8%B1" title="متوقع قدر">متوقع قدر</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ E(X)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>E</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ E(X)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42162ae351644df7e7db492f3083fc61cc99abc9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.146ex; height:2.843ex;" alt="{\displaystyle \ E(X)}"></span> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E(X)=\sum _{x=0}^{n}xp_{X}(x)=np}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <mi>x</mi> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>n</mi> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E(X)=\sum _{x=0}^{n}xp_{X}(x)=np}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/180c021d524be2ecb25afa9136b366d28c0ed438" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:25.338ex; height:6.843ex;" alt="{\displaystyle E(X)=\sum _{x=0}^{n}xp_{X}(x)=np}"></span></dd></dl> <p>تصویر 2 میں سرخ خطِ منحنی کے مطابق <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E(X)=np=40\times 0.5=20}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>n</mi> <mi>p</mi> <mo>=</mo> <mn>40</mn> <mo>×</mo> <mn>0.5</mn> <mo>=</mo> <mn>20</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E(X)=np=40\times 0.5=20}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75daaba9dc71c88f13590df819f19a5ccfa6d027" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.886ex; height:2.843ex;" alt="{\displaystyle E(X)=np=40\times 0.5=20}"></span> </p> <div class="mw-heading mw-heading3"><h3 id="تفاوت"><span id=".D8.AA.D9.81.D8.A7.D9.88.D8.AA"></span>تفاوت</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%AF%D9%88_%D8%B1%D9%82%D9%85%DB%8C_%D8%AA%D9%88%D8%B2%DB%8C%D8%B9&action=edit&section=2" title="تدوینِ قطعہ: تفاوت"><span>ترمیم</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>دو رقمی توزیعِ احتمال شدہ تصادفی متغیر <i>X</i> کا <a href="/wiki/%D8%AA%D9%81%D8%A7%D9%88%D8%AA" title="تفاوت">تفاوت</a> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ {\hbox{var}}(X)=np(1-p)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>var</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>n</mi> <mi>p</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>p</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ {\hbox{var}}(X)=np(1-p)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84c52ab1415a15ea17c280a02df1f73fed11f0ea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.316ex; height:2.843ex;" alt="{\displaystyle \ {\hbox{var}}(X)=np(1-p)}"></span></dd></dl> <p>تصویر 2 میں سرخ خطِ منحنی کے مطابق تَفاوُت <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hbox{var}}(X)=np(1-p)=40\times 0.5\times (1-.5)=10}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>var</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>n</mi> <mi>p</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>40</mn> <mo>×</mo> <mn>0.5</mn> <mo>×</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mn>.5</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mn>10</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hbox{var}}(X)=np(1-p)=40\times 0.5\times (1-.5)=10}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8fd490a1156edd809632f1987ac96578a86a7979" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:46.856ex; height:2.843ex;" alt="{\displaystyle {\hbox{var}}(X)=np(1-p)=40\times 0.5\times (1-.5)=10}"></span> اور <a href="/wiki/%D9%85%D8%B9%DB%8C%D8%A7%D8%B1%DB%8C_%D8%A7%D9%86%D8%AD%D8%B1%D8%A7%D9%81" title="معیاری انحراف">معیاری انحراف</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ {\hbox{std. dev. (X)}}=10^{\frac {1}{2}}\approx 3.16}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>std. dev. (X)</mtext> </mstyle> </mrow> <mo>=</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mo>≈</mo> <mn>3.16</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ {\hbox{std. dev. (X)}}=10^{\frac {1}{2}}\approx 3.16}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40378217e5b7fbdde51324fc4163ac2d16962596" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.646ex; height:4.009ex;" alt="{\displaystyle \ {\hbox{std. dev. (X)}}=10^{\frac {1}{2}}\approx 3.16}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="مزید_دیکھیے"><span id=".D9.85.D8.B2.DB.8C.D8.AF_.D8.AF.DB.8C.DA.A9.DA.BE.DB.8C.DB.92"></span>مزید دیکھیے</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%AF%D9%88_%D8%B1%D9%82%D9%85%DB%8C_%D8%AA%D9%88%D8%B2%DB%8C%D8%B9&action=edit&section=3" title="تدوینِ قطعہ: مزید دیکھیے"><span>ترمیم</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><div style="background-color: #f9f9f9; border: 1px dashed #aaaaaa; padding: .2em; text-align: center; margin: .5em 5em .5em 5em; font-size: large;"><small></small></div></li></ul><small></small><p><small><code>E=mc<sup>2</sup></code>     اردو ویکیپیڈیا پر ریاضی مساوات کو بائیں سے دائیں <small>LTR</small> پڑھیٔے     <a href="https://en.wikipedia.org/wiki/Table_of_mathematical_symbols" class="extiw" title="en:Table of mathematical symbols">ریاضی علامات </a></small> </p> <table class="mbox-small plainlinks sistersitebox" style="border:1px solid #a2a9b1;background-color:#f8f9fa"> <tbody><tr> <td class="mbox-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></td> <td class="mbox-text plainlist">ویکی ذخائر پر <b><a href="https://commons.wikimedia.org/wiki/Category:Binomial_distributions" class="extiw" title="commons:Category:Binomial distributions">دو رقمی توزیع </a></b> سے متعلق سمعی و بصری مواد ملاحظہ کریں۔</td></tr></tbody></table>    </div><noscript><img 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