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class="vector-toc-numb">2</span> <span>Approximationer</span> </div> </a> <ul id="toc-Approximationer-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Exempel" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Exempel"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Exempel</span> </div> </a> <button aria-controls="toc-Exempel-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Växla underavsnittet Exempel</span> </button> <ul id="toc-Exempel-sublist" class="vector-toc-list"> <li id="toc-Exempel_1" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Exempel_1"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Exempel 1</span> </div> </a> <ul id="toc-Exempel_1-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Exempel_2" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Exempel_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Exempel 2</span> </div> </a> <ul id="toc-Exempel_2-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Exempel_3" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Exempel_3"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Exempel 3</span> </div> </a> <ul id="toc-Exempel_3-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Se_även" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Se_även"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Se även</span> </div> </a> <ul id="toc-Se_även-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Externa_länkar" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Externa_länkar"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Externa länkar</span> </div> </a> <ul id="toc-Externa_länkar-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="Innehåll" 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="Växla innehållsförteckningen" > <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">Växla innehållsförteckningen</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">Binomialfördelning</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="Gå till en artikel på ett annat språk. Tillgänglig på 52 språk" > <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 språk</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 – arabiska" lang="ar" hreflang="ar" data-title="توزيع ثنائي الحدين" data-language-autonym="العربية" data-language-local-name="arabiska" class="interlanguage-link-target"><span>العربية</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 – asturiska" lang="ast" hreflang="ast" data-title="Distribución binómica" data-language-autonym="Asturianu" data-language-local-name="asturiska" 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 – bengali" lang="bn" hreflang="bn" data-title="দ্বিপদী বন্টন" data-language-autonym="বাংলা" data-language-local-name="bengali" 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 – belarusiska" lang="be" hreflang="be" data-title="Біномнае размеркаванне" data-language-autonym="Беларуская" data-language-local-name="belarusiska" 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 – katalanska" lang="ca" hreflang="ca" data-title="Distribució binomial" data-language-autonym="Català" data-language-local-name="katalanska" 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 – tjeckiska" lang="cs" hreflang="cs" data-title="Binomické rozdělení" data-language-autonym="Čeština" data-language-local-name="tjeckiska" 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 – danska" lang="da" hreflang="da" data-title="Binomialfordelingen" data-language-autonym="Dansk" data-language-local-name="danska" 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 – tyska" lang="de" hreflang="de" data-title="Binomialverteilung" data-language-autonym="Deutsch" data-language-local-name="tyska" 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 – estniska" lang="et" hreflang="et" data-title="Binoomjaotus" data-language-autonym="Eesti" data-language-local-name="estniska" 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 – grekiska" lang="el" hreflang="el" data-title="Διωνυμική κατανομή" data-language-autonym="Ελληνικά" data-language-local-name="grekiska" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Binomial_distribution" title="Binomial distribution – engelska" lang="en" hreflang="en" data-title="Binomial distribution" data-language-autonym="English" data-language-local-name="engelska" class="interlanguage-link-target"><span>English</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 – spanska" lang="es" hreflang="es" data-title="Distribución binomial" data-language-autonym="Español" data-language-local-name="spanska" 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 – baskiska" lang="eu" hreflang="eu" data-title="Banaketa binomial" data-language-autonym="Euskara" data-language-local-name="baskiska" class="interlanguage-link-target"><span>Euskara</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 – persiska" lang="fa" hreflang="fa" data-title="توزیع دوجمله‌ای" data-language-autonym="فارسی" data-language-local-name="persiska" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr badge-Q17437798 badge-goodarticle mw-list-item" title="bra artikel"><a href="https://fr.wikipedia.org/wiki/Loi_binomiale" title="Loi binomiale – franska" lang="fr" hreflang="fr" data-title="Loi binomiale" data-language-autonym="Français" data-language-local-name="franska" 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 – galiciska" lang="gl" hreflang="gl" data-title="Distribución binomial" data-language-autonym="Galego" data-language-local-name="galiciska" 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 – koreanska" lang="ko" hreflang="ko" data-title="이항 분포" data-language-autonym="한국어" data-language-local-name="koreanska" 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 – hindi" lang="hi" hreflang="hi" data-title="द्विपद वितरण" data-language-autonym="हिन्दी" data-language-local-name="hindi" 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 – indonesiska" lang="id" hreflang="id" data-title="Distribusi binomial" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiska" 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 – italienska" lang="it" hreflang="it" data-title="Distribuzione binomiale" data-language-autonym="Italiano" data-language-local-name="italienska" 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 – hebreiska" lang="he" hreflang="he" data-title="התפלגות בינומית" data-language-autonym="עברית" data-language-local-name="hebreiska" 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 – kazakiska" lang="kk" hreflang="kk" data-title="Биномдық үлестірілу" data-language-autonym="Қазақша" data-language-local-name="kazakiska" 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 – lettiska" lang="lv" hreflang="lv" data-title="Binomiālais sadalījums" data-language-autonym="Latviešu" data-language-local-name="lettiska" 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 – litauiska" lang="lt" hreflang="lt" data-title="Binominis skirstinys" data-language-autonym="Lietuvių" data-language-local-name="litauiska" 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 – ungerska" lang="hu" hreflang="hu" data-title="Binomiális eloszlás" data-language-autonym="Magyar" data-language-local-name="ungerska" 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 – makedonska" lang="mk" hreflang="mk" data-title="Биномна распределба" data-language-autonym="Македонски" data-language-local-name="makedonska" 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 – malajiska" lang="ms" hreflang="ms" data-title="Taburan binomial" data-language-autonym="Bahasa Melayu" data-language-local-name="malajiska" 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 – nederländska" lang="nl" hreflang="nl" data-title="Binomiale verdeling" data-language-autonym="Nederlands" data-language-local-name="nederländska" 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 – japanska" lang="ja" hreflang="ja" data-title="二項分布" data-language-autonym="日本語" data-language-local-name="japanska" 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 – norskt bokmål" lang="nb" hreflang="nb" data-title="Binomisk fordeling" data-language-autonym="Norsk bokmål" data-language-local-name="norskt bokmål" 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 – nynorska" lang="nn" hreflang="nn" data-title="Binomisk fordeling" data-language-autonym="Norsk nynorsk" data-language-local-name="nynorska" 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 – uzbekiska" lang="uz" hreflang="uz" data-title="Binomial taqsimot" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbekiska" 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 – polska" lang="pl" hreflang="pl" data-title="Rozkład dwumianowy" data-language-autonym="Polski" data-language-local-name="polska" 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 – portugisiska" lang="pt" hreflang="pt" data-title="Distribuição binomial" data-language-autonym="Português" data-language-local-name="portugisiska" 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 – rumänska" lang="ro" hreflang="ro" data-title="Distribuția binomială" data-language-autonym="Română" data-language-local-name="rumänska" 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 – ryska" lang="ru" hreflang="ru" data-title="Биномиальное распределение" data-language-autonym="Русский" data-language-local-name="ryska" 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 – albanska" lang="sq" hreflang="sq" data-title="Shpërndarja binomiale" data-language-autonym="Shqip" data-language-local-name="albanska" 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 – slovakiska" lang="sk" hreflang="sk" data-title="Binomické rozdelenie" data-language-autonym="Slovenčina" data-language-local-name="slovakiska" 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 – slovenska" lang="sl" hreflang="sl" data-title="Binomska porazdelitev" data-language-autonym="Slovenščina" data-language-local-name="slovenska" 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 – serbiska" lang="sr" hreflang="sr" data-title="Binomna raspodela" data-language-autonym="Српски / srpski" data-language-local-name="serbiska" 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 – sundanesiska" lang="su" hreflang="su" data-title="Sebaran binomial" data-language-autonym="Sunda" data-language-local-name="sundanesiska" 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 – finska" lang="fi" hreflang="fi" data-title="Binomijakauma" data-language-autonym="Suomi" data-language-local-name="finska" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Distribusyong_binomial" title="Distribusyong binomial – tagalog" lang="tl" hreflang="tl" data-title="Distribusyong binomial" data-language-autonym="Tagalog" data-language-local-name="tagalog" 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 – tamil" lang="ta" hreflang="ta" data-title="ஈருறுப்புப் பரவல்" data-language-autonym="தமிழ்" data-language-local-name="tamil" 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 – thailändska" lang="th" hreflang="th" data-title="การแจกแจงทวินาม" data-language-autonym="ไทย" data-language-local-name="thailändska" 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 – turkiska" lang="tr" hreflang="tr" data-title="Binom dağılımı" data-language-autonym="Türkçe" data-language-local-name="turkiska" 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 – ukrainska" lang="uk" hreflang="uk" data-title="Біноміальний розподіл" data-language-autonym="Українська" data-language-local-name="ukrainska" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%AF%D9%88_%D8%B1%D9%82%D9%85%DB%8C_%D8%AA%D9%88%D8%B2%DB%8C%D8%B9" title="دو رقمی توزیع – urdu" lang="ur" hreflang="ur" data-title="دو رقمی توزیع" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</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 – vietnamesiska" lang="vi" hreflang="vi" data-title="Phân phối nhị thức" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamesiska" 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 – kantonesiska" lang="yue" 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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">Från Wikipedia</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-ltr mw-parser-output" lang="sv" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r51224235">.mw-parser-output table.ambox{margin:0 10%;border-collapse:collapse;background:#fbfbfb;border:1px solid #aaa;border-left:10px solid #608ec2}.mw-parser-output table.ambox th.ambox-text,.mw-parser-output table.ambox td.ambox-text{padding:.25em .5em;width:100%}.mw-parser-output table.ambox td.ambox-image{padding:2px 0 2px .5em;text-align:center;vertical-align:middle}.mw-parser-output table.ambox td.ambox-imageright{padding:2px 4px 2px 0;text-align:center;vertical-align:middle}.mw-parser-output table.ambox-notice{border-left:10px solid #608ec2}.mw-parser-output table.ambox-delete,.mw-parser-output table.ambox-serious{border-left:10px solid #b22222}.mw-parser-output table.ambox-content{border-left:10px solid #f28500}.mw-parser-output table.ambox-style{border-left:10px solid #f4c430}.mw-parser-output table.ambox-merge{border-left:10px solid #9932cc}.mw-parser-output table.ambox-protection{border-left:10px solid #bba}.mw-parser-output .ambox+link+.ambox{border-top-width:0}.mw-parser-output .messagebox{border:1px solid #aaaaaa;background-color:#f8f9fa;width:80%;margin:0 auto 1em auto;padding:.2em}.mw-parser-output .messagebox.merge{border:1px solid #c0b8cc;background-color:#f0e5ff;text-align:center}.mw-parser-output .messagebox.cleanup{border:1px solid #9f9fff;background-color:#efefff;text-align:center}.mw-parser-output .messagebox.standard-talk{border:1px solid #c0c090;background-color:#f8eaba}.mw-parser-output .messagebox.nested-talk{border:1px solid #c0c090;background-color:#f8eaba;width:100%;margin:2px 4px}</style><table class="metadata ambox ambox-content" style=""> <tbody><tr> <td class="ambox-image"> <div style="width:52px;"><span typeof="mw:File"><a href="/wiki/Fil:Question_book-4.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/40px-Question_book-4.svg.png" decoding="async" width="40" height="31" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/60px-Question_book-4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/80px-Question_book-4.svg.png 2x" data-file-width="262" data-file-height="204" /></a></span></div></td> <td class="ambox-text">Den här artikeln <b>behöver <a href="/wiki/Wikipedia:K%C3%A4llh%C3%A4nvisningar" title="Wikipedia:Källhänvisningar">källhänvisningar</a> för att kunna <a href="/wiki/Wikipedia:Verifierbarhet" title="Wikipedia:Verifierbarhet">verifieras</a>.</b> <small>(2020-12)</small> <br /><small>Åtgärda genom att lägga till pålitliga källor (<a href="/wiki/Wikipedia:Introduktion_till_k%C3%A4llh%C3%A4nvisningar" title="Wikipedia:Introduktion till källhänvisningar">gärna som fotnoter</a>). Uppgifter utan källhänvisning kan <a href="/wiki/Mall:K%C3%A4lla_beh%C3%B6vs" title="Mall:Källa behövs">ifrågasättas</a> och tas bort utan att det behöver diskuteras på <a href="/wiki/Diskussion:Binomialf%C3%B6rdelning" title="Diskussion:Binomialfördelning">diskussionssidan</a>.</small></td> </tr> </tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fil:Galton_Box.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/Galton_Box.svg/250px-Galton_Box.svg.png" decoding="async" width="250" height="295" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/Galton_Box.svg/375px-Galton_Box.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/78/Galton_Box.svg/500px-Galton_Box.svg.png 2x" data-file-width="660" data-file-height="780" /></a><figcaption>Galtons bräda ger en binomialfördelning.</figcaption></figure> <p>En <b>binomialfördelning</b> är inom <a href="/wiki/Sannolikhetsteori" title="Sannolikhetsteori">sannolikhetsteori</a> och <a href="/wiki/Matematisk_statistik" title="Matematisk statistik">matematisk statistik</a> en <a href="/wiki/Diskret" class="mw-redirect" title="Diskret">diskret</a> <a href="/wiki/Sannolikhetsf%C3%B6rdelning" title="Sannolikhetsfördelning">fördelning</a> som uppkommer genom upprepade (diskreta) försök där en specifik händelse har samma <a href="/wiki/Sannolikhet" title="Sannolikhet">sannolikhet</a> i varje försök. </p><p>Vid till exempel dragning ur <a href="/wiki/Urnmodell" title="Urnmodell">urna</a> måste <a href="/wiki/Dragning_med_%C3%A5terl%C3%A4ggning" title="Dragning med återläggning">dragning med återläggning</a> ske vilket är ett villkor för att binomialfördelningens <a href="/wiki/T%C3%A4thetsfunktion" title="Täthetsfunktion">täthetsfunktion</a> skall gälla, vilket också är det villkor som skiljer binomialfördelningen från den <a href="/wiki/Hypergeometrisk_f%C3%B6rdelning" title="Hypergeometrisk fördelning">hypergeometriska fördelningen</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binomialf%C3%B6rdelning&veaction=edit&section=1" title="Redigera avsnitt: Definition" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Binomialf%C3%B6rdelning&action=edit&section=1" title="Redigera avsnitts källkod: Definition"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fil:Binomial_Distribution.PNG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Binomial_Distribution.PNG/250px-Binomial_Distribution.PNG" decoding="async" width="250" height="155" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Binomial_Distribution.PNG/375px-Binomial_Distribution.PNG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Binomial_Distribution.PNG/500px-Binomial_Distribution.PNG 2x" data-file-width="1000" data-file-height="618" /></a><figcaption>Binomialfördelning med parametern <i>p</i> 0,1 (blå), 0,5 (grön) och 0,8 (röd) samt <i>n</i> 20.</figcaption></figure> <p>Om en <a href="/wiki/Stokastisk" class="mw-redirect" title="Stokastisk">stokastisk</a> variabel (en funktion från utfallsrummet till <b>R</b><sup>1</sup>) <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 X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> är binomialfördelad och <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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> är antalet utfall och <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> är sannolikheten för en viss händelse för varje utfall, skrivs detta som </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 X\in \mathrm {Bin} (n,p)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> </mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>,</mo> <mi>p</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X\in \mathrm {Bin} (n,p)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/282a7eaad69124189a7c991e02224a699f7b8fab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.813ex; height:2.843ex;" alt="{\displaystyle X\in \mathrm {Bin} (n,p)}"></span></dd></dl> <p>och har <a href="/wiki/Sannolikhetsfunktion" title="Sannolikhetsfunktion">sannolikhetsfunktionen</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 p_{X}(k)=P(X=k)={n \choose k}p^{k}(1-p)^{n-k}}"> <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>k</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>P</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo>=</mo> <mi>k</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em">(</mo> </mrow> <mfrac linethickness="0"> <mi>n</mi> <mi>k</mi> </mfrac> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">)</mo> </mrow> </mrow> </mrow> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</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>k</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{X}(k)=P(X=k)={n \choose k}p^{k}(1-p)^{n-k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae6e92761aa31191d268139a2bd79f09b5109790" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; margin-left: -0.089ex; width:39.362ex; height:6.176ex;" alt="{\displaystyle p_{X}(k)=P(X=k)={n \choose k}p^{k}(1-p)^{n-k}}"></span></dd></dl> <p>vilken anger sannolikheten för <i>k</i> utfall av händelsen vars <a href="/wiki/Sannolikhet" title="Sannolikhet">sannolikhet</a> är <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> och där <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"> <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/9633a8692121eedfa99cace406205e5d1511ef8d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.172ex; height:2.509ex;" alt="{\displaystyle 1-p}"></span> är sannolikheten för händelsens komplement, det vill säga, sannolikheten att händelsen <i>inte</i> inträffar. Skrivsättet med två tal ovanför varandra i en parentes betecknar så kallade <a href="/wiki/Binomialkoefficient" title="Binomialkoefficient">binomialkoefficienter</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Approximationer">Approximationer</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binomialf%C3%B6rdelning&veaction=edit&section=2" title="Redigera avsnitt: Approximationer" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Binomialf%C3%B6rdelning&action=edit&section=2" title="Redigera avsnitts källkod: Approximationer"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Binomialfördelningen, Bin(n, p), kan under vissa villkor approximeras med andra fördelningar. </p> <table class="wikitable" width="600"> <tbody><tr> <th>Approximation </th> <th>Krav </th> <th>Namn </th></tr> <tr> <td><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 \mathrm {Po} (np)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">o</mi> </mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mi>p</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Po} (np)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18d896bf85961a35c4e7a4dbd129459f562fd655" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.119ex; height:2.843ex;" alt="{\displaystyle \mathrm {Po} (np)}"></span> </td> <td><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 n>10,p\leq 0.1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>></mo> <mn>10</mn> <mo>,</mo> <mi>p</mi> <mo>≤</mo> <mn>0.1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n>10,p\leq 0.1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36a0ca291717b44bd498e09aa66ac95d0d62c371" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.092ex; height:2.509ex;" alt="{\displaystyle n>10,p\leq 0.1}"></span> </td> <td><a href="/wiki/Poissonf%C3%B6rdelning" title="Poissonfördelning">Poissonfördelning</a> </td></tr> <tr> <td><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 N(np,{\sqrt {np(1-p)}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mi>p</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>n</mi> <mi>p</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>p</mi> <mo stretchy="false">)</mo> </msqrt> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N(np,{\sqrt {np(1-p)}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/baebdaebb08490fb93c3a858e4422678c000910c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:19.34ex; height:4.843ex;" alt="{\displaystyle N(np,{\sqrt {np(1-p)}})}"></span> </td> <td><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 np(1-p)\geq 10}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <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>10</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle np(1-p)\geq 10}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/900202d5d84b7b4318e5f78ed4699b5d11366a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.969ex; height:2.843ex;" alt="{\displaystyle np(1-p)\geq 10}"></span> </td> <td><a href="/wiki/Normalf%C3%B6rdelning" title="Normalfördelning">Normalfördelning</a> </td></tr></tbody></table> <p>Dessutom kan den <a href="/wiki/Hypergeometrisk_f%C3%B6rdelning" title="Hypergeometrisk fördelning">hypergeometriska fördelningen</a> Hyp(<i>N</i>, <i>n</i>, <i>p</i>) approximeras till Bin(<i>n</i>, <i>p</i>) om <i>N</i> är mycket stort i förhållande till <i>n</i>, <i>n</i>/<i>N</i> ≤ 0,1. </p> <div class="mw-heading mw-heading2"><h2 id="Exempel">Exempel</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binomialf%C3%B6rdelning&veaction=edit&section=3" title="Redigera avsnitt: Exempel" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Binomialf%C3%B6rdelning&action=edit&section=3" title="Redigera avsnitts källkod: Exempel"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Exempel_1">Exempel 1</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binomialf%C3%B6rdelning&veaction=edit&section=4" title="Redigera avsnitt: Exempel 1" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Binomialf%C3%B6rdelning&action=edit&section=4" title="Redigera avsnitts källkod: Exempel 1"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ett slag av <a href="/wiki/Urnmodell" title="Urnmodell">urnmodell</a> är urnor med svarta och vita kulor. Sannolikheten att dra en vit kula vid en <a href="/wiki/Slumpm%C3%A4ssig" class="mw-redirect" title="Slumpmässig">slumpmässig</a> dragning är <i>p</i>. Sannolikheten att man drar exakt <i>k</i> stycken vita kulor vid <i>n</i> försök om man har <i>s</i> stycken svarta och <i>v</i> st vita kulor i en urna och <i>lägger tillbaka</i> kulorna mellan dragningarna (<a href="/wiki/Dragning_med_%C3%A5terl%C3%A4ggning" title="Dragning med återläggning">dragning med återläggning</a>) ges då av täthetsfunktionen ovan med </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={v \over {s+v}}\quad {\text{och}}\quad q=1-p,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mo>+</mo> <mi>v</mi> </mrow> </mfrac> </mrow> <mspace width="1em" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>och</mtext> </mrow> <mspace width="1em" /> <mi>q</mi> <mo>=</mo> <mn>1</mn> <mo>−</mo> <mi>p</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p={v \over {s+v}}\quad {\text{och}}\quad q=1-p,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c474d124a065b3a7f1cf4c51c8e5a54e19fdc8f9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; margin-left: -0.089ex; width:28.372ex; height:4.843ex;" alt="{\displaystyle p={v \over {s+v}}\quad {\text{och}}\quad q=1-p,}"></span></dd></dl> <p>där <i>p</i> och <i>q</i> ges genom den <a href="/wiki/Klassisk_sannolikhetsdefinition" title="Klassisk sannolikhetsdefinition">klassiska sannolikhetsdefinitionen</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Exempel_2">Exempel 2</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binomialf%C3%B6rdelning&veaction=edit&section=5" title="Redigera avsnitt: Exempel 2" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Binomialf%C3%B6rdelning&action=edit&section=5" title="Redigera avsnitts källkod: Exempel 2"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Om man kastar en tärning tre gånger och sannolikheten att få en sexa är 1/6, blir sannolikheten att få sexa två gånger </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={3 \choose 2}\left({1 \over 6}\right)^{2}{5 \over 6}={5 \over 72}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em">(</mo> </mrow> <mfrac linethickness="0"> <mn>3</mn> <mn>2</mn> </mfrac> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">)</mo> </mrow> </mrow> </mrow> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>5</mn> <mn>6</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>5</mn> <mn>72</mn> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P={3 \choose 2}\left({1 \over 6}\right)^{2}{5 \over 6}={5 \over 72}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a900cfcf35c33af08f2305b42c34ad2c40b44716" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:24.806ex; height:6.509ex;" alt="{\displaystyle P={3 \choose 2}\left({1 \over 6}\right)^{2}{5 \over 6}={5 \over 72}.}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Exempel_3">Exempel 3</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binomialf%C3%B6rdelning&veaction=edit&section=6" title="Redigera avsnitt: Exempel 3" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Binomialf%C3%B6rdelning&action=edit&section=6" title="Redigera avsnitts källkod: Exempel 3"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>På samma sätt kan sannolikheten beräknas för att vid <i>n</i> kast få siffran sex <i>n</i> gånger: </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={n \choose n}\left({1 \over 6}\right)^{n}\left({5 \over 6}\right)^{n-n}=\left({1 \over 6}\right)^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em">(</mo> </mrow> <mfrac linethickness="0"> <mi>n</mi> <mi>n</mi> </mfrac> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">)</mo> </mrow> </mrow> </mrow> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>5</mn> <mn>6</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mi>n</mi> </mrow> </msup> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P={n \choose n}\left({1 \over 6}\right)^{n}\left({5 \over 6}\right)^{n-n}=\left({1 \over 6}\right)^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1003b3726f3f200d271d99f6e6f2ebbecfb04a8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:34.938ex; height:6.509ex;" alt="{\displaystyle P={n \choose n}\left({1 \over 6}\right)^{n}\left({5 \over 6}\right)^{n-n}=\left({1 \over 6}\right)^{n}}"></span></dd></dl> <p>vilket är rimligt då det rör sig om <i>n</i> oberoende <a href="/wiki/Utfall" title="Utfall">utfall</a> som vardera har sannolikheten 1/6. </p> <div class="mw-heading mw-heading2"><h2 id="Se_även"><span id="Se_.C3.A4ven"></span>Se även</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binomialf%C3%B6rdelning&veaction=edit&section=7" title="Redigera avsnitt: Se även" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Binomialf%C3%B6rdelning&action=edit&section=7" title="Redigera avsnitts källkod: Se även"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Binomialsatsen" title="Binomialsatsen">Binomialsatsen</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Externa_länkar"><span id="Externa_l.C3.A4nkar"></span>Externa länkar</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binomialf%C3%B6rdelning&veaction=edit&section=8" title="Redigera avsnitt: Externa länkar" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Binomialf%C3%B6rdelning&action=edit&section=8" title="Redigera avsnitts källkod: Externa länkar"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/15px-Commons-logo.svg.png" decoding="async" width="15" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/23px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> Wikimedia Commons har media som rör <a href="https://commons.wikimedia.org/wiki/Category:Binomial_distributions" class="extiw" title="commons:Category:Binomial distributions">Binomialfördelning</a>.<div class="interProject commons" style="display:none;"><a href="https://commons.wikimedia.org/wiki/Category:Binomial_distributions" class="extiw" title="commons:Category:Binomial distributions">Bilder & media</a></div></li></ul> <style data-mw-deduplicate="TemplateStyles:r56287950">.mw-parser-output table.navbox{border:#aaa 1px solid;width:100%;margin:auto;margin-top:1em;clear:both;font-size:88%;text-align:center;padding:1px}.mw-parser-output link+table.navbox{margin-top:-1px}.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow,.mw-parser-output table.navbox th{text-align:center;padding-left:1em;padding-right:1em}.mw-parser-output .navbox-thlinkcolor .navbox-title button,.mw-parser-output .navbox-thlinkcolor .navbox-title .mw-collapsible-text,.mw-parser-output .navbox-thlinkcolor .navbox-title a{color:inherit}.mw-parser-output .nowraplinks a,.mw-parser-output .nowraplinks .selflink{white-space:nowrap}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right;font-weight:bold;padding-left:1em;padding-right:1em}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background:#fdfdfd}.mw-parser-output .navbox-list{border-color:#fdfdfd}.mw-parser-output .navbox-title,.mw-parser-output table.navbox th{background:#b0c4de}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background:#d0e0f5}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background:#deeafa}.mw-parser-output .navbox-even{background:#f7f7f7}.mw-parser-output .navbox-odd{background:transparent}</style><table class="navbox" style="border-spacing:0; ;"><tbody><tr><td style="padding:2px;"><table class="collapsible autocollapse" style="width:100%;border-spacing:0;background:transparent;color:inherit;;"><tbody><tr><th style=";" colspan="2" class="navbox-title"><div style="float:left; width:3em;text-align:left;"><div class="noprint plainlinks" style="background-color:transparent; padding:0; white-space:nowrap; font-weight:normal; font-size:80%; border:none;; color: inherit;"><a href="/wiki/Mall:Sannolikhetsf%C3%B6rdelningar" title="Mall:Sannolikhetsfördelningar"><span title="Visa denna mall" style="border:none;;">v</span></a> <span style="font-size:80%;">•</span> <a class="external text" href="https://sv.wikipedia.org/w/index.php?title=Mall:Sannolikhetsf%C3%B6rdelningar&action=edit"><span style="border:none;;" title="Redigera den här mallen">r</span></a></div></div><span style="font-size:110%;"><a href="/wiki/Sannolikhetsf%C3%B6rdelning" title="Sannolikhetsfördelning">Sannolikhetsfördelningar</a></span></th></tr><tr style="height:2px;"><td></td></tr><tr><td class="navbox-group" style=";;">Diskreta</td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a href="/wiki/Bernoullif%C3%B6rdelning" title="Bernoullifördelning">Bernoulli</a> <span style="font-weight:bold;"> · </span> <a class="mw-selflink selflink">Binomial</a><span style="font-weight:bold;"> · </span><a href="/wiki/Hypergeometrisk_f%C3%B6rdelning" title="Hypergeometrisk fördelning">Hypergeometrisk</a><span style="font-weight:bold;"> · </span><a href="/wiki/Negativ_binomialf%C3%B6rdelning" title="Negativ binomialfördelning">Negativ binomial</a><span style="font-weight:bold;"> · </span><a href="/wiki/Poissonf%C3%B6rdelning" title="Poissonfördelning">Poisson</a></div></td></tr><tr style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";;">Kontinuerliga</td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a href="/wiki/Betaf%C3%B6rdelning" title="Betafördelning">Beta</a><span style="font-weight:bold;"> · </span><a href="/wiki/Cauchyf%C3%B6rdelning" title="Cauchyfördelning">Cauchy</a><span style="font-weight:bold;"> · </span><a href="/wiki/Chitv%C3%A5f%C3%B6rdelning" title="Chitvåfördelning">Chitvå</a><span style="font-weight:bold;"> · </span><a href="/wiki/Exponentialf%C3%B6rdelning" title="Exponentialfördelning">Exponential</a><span style="font-weight:bold;"> · </span><a href="/wiki/Gammaf%C3%B6rdelning" title="Gammafördelning">Gamma</a><span style="font-weight:bold;"> · </span><a href="/wiki/Likformig_f%C3%B6rdelning" class="mw-redirect" title="Likformig fördelning">Likformig</a><span style="font-weight:bold;"> · </span><a href="/wiki/Lognormalf%C3%B6rdelning" title="Lognormalfördelning">Lognormal</a><span style="font-weight:bold;"> · </span><a href="/wiki/Maxwell%E2%80%93Boltzmannf%C3%B6rdelning" title="Maxwell–Boltzmannfördelning">Maxwell–Boltzmann</a><span style="font-weight:bold;"> · </span><a href="/wiki/Normalf%C3%B6rdelning" title="Normalfördelning">Normal</a><span style="font-weight:bold;"> · </span><a href="/wiki/Rayleighf%C3%B6rdelning" title="Rayleighfördelning">Rayleigh</a><span style="font-weight:bold;"> · </span><a href="/wiki/Students_t-f%C3%B6rdelning" title="Students t-fördelning">Students t</a><span style="font-weight:bold;"> · </span><a href="/wiki/Weibullf%C3%B6rdelning" title="Weibullfördelning">Weibull</a></div></td></tr></tbody></table></td></tr></tbody></table>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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