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class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%9B%D7%A0%D7%99%D7%A1%D7%94_%D7%9C%D7%97%D7%A9%D7%91%D7%95%D7%9F&returnto=%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="מומלץ להיכנס לחשבון, אך אין חובה לעשות זאת [o]" accesskey="o" class=""><span>כניסה לחשבון</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="אפשרויות נוספות" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="כלים אישיים" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">כלים אישיים</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="תפריט משתמש" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_he.wikipedia.org&uselang=he"><span>תרומה לוויקיפדיה</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%94%D7%A8%D7%A9%D7%9E%D7%94_%D7%9C%D7%97%D7%A9%D7%91%D7%95%D7%9F&returnto=%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="מומלץ ליצור חשבון ולהיכנס אליו, אך אין חובה לעשות זאת"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>יצירת חשבון</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%9B%D7%A0%D7%99%D7%A1%D7%94_%D7%9C%D7%97%D7%A9%D7%91%D7%95%D7%9F&returnto=%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="מומלץ להיכנס לחשבון, אך אין חובה לעשות זאת [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>כניסה לחשבון</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 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href=\"/wiki/%D7%95%D7%99%D7%A7%D7%99%D7%A4%D7%93%D7%99%D7%94:%D7%9E%D7%99%D7%96%D7%9E%D7%99_%D7%95%D7%99%D7%A7%D7%99%D7%A4%D7%93%D7%99%D7%94/%D7%92%D7%9C%D7%90%D7%9D/%D7%94%D7%A1%D7%A4%D7%A8%D7%99%D7%99%D7%94_%D7%94%D7%9C%D7%90%D7%95%D7%9E%D7%99%D7%AA/%D7%90%D7%99%D7%A8%D7%95%D7%A2%D7%99%D7%9D/%D7%A1%D7%93%D7%A0%D7%AA_%D7%A2%D7%A8%D7%99%D7%9B%D7%94_%D7%93%D7%A6%D7%9E%D7%91%D7%A8_2024\" title=\"ויקיפדיה:מיזמי ויקיפדיה/גלאם/הספרייה הלאומית/אירועים/סדנת עריכה דצמבר 2024\"\u003Eכאן\u003C/a\u003E.\u003C/b\u003E\n\u003C/p\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E";}}());</script></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="אתר"> <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="תוכן עניינים" 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">תוכן עניינים</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">העברה לסרגל הצד</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">הסתרה</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">התחלה</div> </a> </li> <li id="toc-ההתפלגות_הבינומית" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#ההתפלגות_הבינומית"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>ההתפלגות הבינומית</span> </div> </a> <button aria-controls="toc-ההתפלגות_הבינומית-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>שינוי מצב התת־פרק ההתפלגות הבינומית</span> </button> <ul id="toc-ההתפלגות_הבינומית-sublist" class="vector-toc-list"> <li id="toc-סכום_ההסתברויות" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#סכום_ההסתברויות"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>סכום ההסתברויות</span> </div> </a> <ul id="toc-סכום_ההסתברויות-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-תוחלת_ושונות" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#תוחלת_ושונות"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>תוחלת ושונות</span> </div> </a> <ul id="toc-תוחלת_ושונות-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-דוגמה" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#דוגמה"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>דוגמה</span> </div> </a> <ul id="toc-דוגמה-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-התפלגות_בינומית_שלילית" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#התפלגות_בינומית_שלילית"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>התפלגות בינומית שלילית</span> </div> </a> <ul id="toc-התפלגות_בינומית_שלילית-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-קשרים_להתפלגויות_אחרות" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#קשרים_להתפלגויות_אחרות"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>קשרים להתפלגויות אחרות</span> </div> </a> <button aria-controls="toc-קשרים_להתפלגויות_אחרות-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>שינוי מצב התת־פרק קשרים להתפלגויות אחרות</span> </button> <ul id="toc-קשרים_להתפלגויות_אחרות-sublist" class="vector-toc-list"> <li id="toc-סכום_של_משתנים_מקריים_בינומיים" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#סכום_של_משתנים_מקריים_בינומיים"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>סכום של משתנים מקריים בינומיים</span> </div> </a> <ul id="toc-סכום_של_משתנים_מקריים_בינומיים-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-התפלגות_ברנולי" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#התפלגות_ברנולי"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>התפלגות ברנולי</span> </div> </a> <ul id="toc-התפלגות_ברנולי-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-קירוב_על_ידי_התפלגות_פואסון" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#קירוב_על_ידי_התפלגות_פואסון"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>קירוב על ידי התפלגות פואסון</span> </div> </a> <ul id="toc-קירוב_על_ידי_התפלגות_פואסון-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-קירוב_על_ידי_התפלגות_נורמלית" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#קירוב_על_ידי_התפלגות_נורמלית"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>קירוב על ידי התפלגות נורמלית</span> </div> </a> <ul id="toc-קירוב_על_ידי_התפלגות_נורמלית-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-התפלגויות_קשורות" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#התפלגויות_קשורות"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>התפלגויות קשורות</span> </div> </a> <ul id="toc-התפלגויות_קשורות-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-ראו_גם" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#ראו_גם"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>ראו גם</span> </div> </a> <ul id="toc-ראו_גם-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-קישורים_חיצוניים" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#קישורים_חיצוניים"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>קישורים חיצוניים</span> </div> </a> <ul id="toc-קישורים_חיצוניים-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="תוכן עניינים" 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="מצב תוכן העניינים" > <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">מצב תוכן העניינים</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">התפלגות בינומית</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="מעבר לערך בשפה אחרת. זמין ב־52 שפות" > <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 שפות</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Binomial_distribution" title="Binomial distribution – אנגלית" lang="en" hreflang="en" data-title="Binomial distribution" data-language-autonym="English" data-language-local-name="אנגלית" class="interlanguage-link-target"><span>English</span></a></li><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 – ערבית" lang="ar" hreflang="ar" data-title="توزيع ثنائي الحدين" data-language-autonym="العربية" data-language-local-name="ערבית" 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 – אסטורית" lang="ast" hreflang="ast" data-title="Distribución binómica" data-language-autonym="Asturianu" data-language-local-name="אסטורית" class="interlanguage-link-target"><span>Asturianu</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 – בלארוסית" lang="be" hreflang="be" data-title="Біномнае размеркаванне" data-language-autonym="Беларуская" data-language-local-name="בלארוסית" class="interlanguage-link-target"><span>Беларуская</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 – בנגלית" lang="bn" hreflang="bn" data-title="দ্বিপদী বন্টন" data-language-autonym="বাংলা" data-language-local-name="בנגלית" class="interlanguage-link-target"><span>বাংলা</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 – קטלאנית" lang="ca" hreflang="ca" data-title="Distribució binomial" data-language-autonym="Català" data-language-local-name="קטלאנית" 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 – צ׳כית" lang="cs" hreflang="cs" data-title="Binomické rozdělení" data-language-autonym="Čeština" data-language-local-name="צ׳כית" 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 – דנית" lang="da" hreflang="da" data-title="Binomialfordelingen" data-language-autonym="Dansk" data-language-local-name="דנית" 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 – גרמנית" lang="de" hreflang="de" data-title="Binomialverteilung" data-language-autonym="Deutsch" data-language-local-name="גרמנית" class="interlanguage-link-target"><span>Deutsch</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 – יוונית" lang="el" hreflang="el" data-title="Διωνυμική κατανομή" data-language-autonym="Ελληνικά" data-language-local-name="יוונית" 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 – ספרדית" lang="es" hreflang="es" data-title="Distribución binomial" data-language-autonym="Español" data-language-local-name="ספרדית" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Binoomjaotus" title="Binoomjaotus – אסטונית" lang="et" hreflang="et" data-title="Binoomjaotus" data-language-autonym="Eesti" data-language-local-name="אסטונית" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Banaketa_binomial" title="Banaketa binomial – בסקית" lang="eu" hreflang="eu" data-title="Banaketa binomial" data-language-autonym="Euskara" data-language-local-name="בסקית" 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 – פרסית" lang="fa" hreflang="fa" data-title="توزیع دوجمله‌ای" data-language-autonym="فارسی" data-language-local-name="פרסית" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Binomijakauma" title="Binomijakauma – פינית" lang="fi" hreflang="fi" data-title="Binomijakauma" data-language-autonym="Suomi" data-language-local-name="פינית" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr badge-Q17437798 badge-goodarticle mw-list-item" title="ערך טוב"><a href="https://fr.wikipedia.org/wiki/Loi_binomiale" title="Loi binomiale – צרפתית" lang="fr" hreflang="fr" data-title="Loi binomiale" data-language-autonym="Français" data-language-local-name="צרפתית" 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 – גליסית" lang="gl" hreflang="gl" data-title="Distribución binomial" data-language-autonym="Galego" data-language-local-name="גליסית" class="interlanguage-link-target"><span>Galego</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 – הינדי" lang="hi" hreflang="hi" data-title="द्विपद वितरण" data-language-autonym="हिन्दी" data-language-local-name="הינדי" class="interlanguage-link-target"><span>हिन्दी</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 – הונגרית" lang="hu" hreflang="hu" data-title="Binomiális eloszlás" data-language-autonym="Magyar" data-language-local-name="הונגרית" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Distribusi_binomial" title="Distribusi binomial – אינדונזית" lang="id" hreflang="id" data-title="Distribusi binomial" data-language-autonym="Bahasa Indonesia" data-language-local-name="אינדונזית" 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 – איטלקית" lang="it" hreflang="it" data-title="Distribuzione binomiale" data-language-autonym="Italiano" data-language-local-name="איטלקית" class="interlanguage-link-target"><span>Italiano</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 – יפנית" lang="ja" hreflang="ja" data-title="二項分布" data-language-autonym="日本語" data-language-local-name="יפנית" class="interlanguage-link-target"><span>日本語</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 – קזחית" lang="kk" hreflang="kk" data-title="Биномдық үлестірілу" data-language-autonym="Қазақша" data-language-local-name="קזחית" class="interlanguage-link-target"><span>Қазақша</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 – קוריאנית" lang="ko" hreflang="ko" data-title="이항 분포" data-language-autonym="한국어" data-language-local-name="קוריאנית" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Binominis_skirstinys" title="Binominis skirstinys – ליטאית" lang="lt" hreflang="lt" data-title="Binominis skirstinys" data-language-autonym="Lietuvių" data-language-local-name="ליטאית" class="interlanguage-link-target"><span>Lietuvių</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 – לטבית" lang="lv" hreflang="lv" data-title="Binomiālais sadalījums" data-language-autonym="Latviešu" data-language-local-name="לטבית" class="interlanguage-link-target"><span>Latviešu</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 – מקדונית" lang="mk" hreflang="mk" data-title="Биномна распределба" data-language-autonym="Македонски" data-language-local-name="מקדונית" 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 – מלאית" lang="ms" hreflang="ms" data-title="Taburan binomial" data-language-autonym="Bahasa Melayu" data-language-local-name="מלאית" 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 – הולנדית" lang="nl" hreflang="nl" data-title="Binomiale verdeling" data-language-autonym="Nederlands" data-language-local-name="הולנדית" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Binomisk_fordeling" title="Binomisk fordeling – נורווגית חדשה" lang="nn" hreflang="nn" data-title="Binomisk fordeling" data-language-autonym="Norsk nynorsk" data-language-local-name="נורווגית חדשה" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Binomisk_fordeling" title="Binomisk fordeling – נורווגית ספרותית" lang="nb" hreflang="nb" data-title="Binomisk fordeling" data-language-autonym="Norsk bokmål" data-language-local-name="נורווגית ספרותית" class="interlanguage-link-target"><span>Norsk bokmål</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 – פולנית" lang="pl" hreflang="pl" data-title="Rozkład dwumianowy" data-language-autonym="Polski" data-language-local-name="פולנית" 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 – פורטוגזית" lang="pt" hreflang="pt" data-title="Distribuição binomial" data-language-autonym="Português" data-language-local-name="פורטוגזית" 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 – רומנית" lang="ro" hreflang="ro" data-title="Distribuția binomială" data-language-autonym="Română" data-language-local-name="רומנית" 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 – רוסית" lang="ru" hreflang="ru" data-title="Биномиальное распределение" data-language-autonym="Русский" data-language-local-name="רוסית" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Binomial_distribution" title="Binomial distribution – אנגלית פשוטה" lang="en-simple" hreflang="en-simple" data-title="Binomial distribution" data-language-autonym="Simple English" data-language-local-name="אנגלית פשוטה" 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 – סלובקית" lang="sk" hreflang="sk" data-title="Binomické rozdelenie" data-language-autonym="Slovenčina" data-language-local-name="סלובקית" 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 – סלובנית" lang="sl" hreflang="sl" data-title="Binomska porazdelitev" data-language-autonym="Slovenščina" data-language-local-name="סלובנית" class="interlanguage-link-target"><span>Slovenščina</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 – אלבנית" lang="sq" hreflang="sq" data-title="Shpërndarja binomiale" data-language-autonym="Shqip" data-language-local-name="אלבנית" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Binomna_raspodela" title="Binomna raspodela – סרבית" lang="sr" hreflang="sr" data-title="Binomna raspodela" data-language-autonym="Српски / srpski" data-language-local-name="סרבית" 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 – סונדנזית" lang="su" hreflang="su" data-title="Sebaran binomial" data-language-autonym="Sunda" data-language-local-name="סונדנזית" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Binomialf%C3%B6rdelning" title="Binomialfördelning – שוודית" lang="sv" hreflang="sv" data-title="Binomialfördelning" data-language-autonym="Svenska" data-language-local-name="שוודית" class="interlanguage-link-target"><span>Svenska</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 – טמילית" lang="ta" hreflang="ta" data-title="ஈருறுப்புப் பரவல்" data-language-autonym="தமிழ்" data-language-local-name="טמילית" 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 – תאית" lang="th" hreflang="th" data-title="การแจกแจงทวินาม" data-language-autonym="ไทย" data-language-local-name="תאית" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Distribusyong_binomial" title="Distribusyong binomial – טאגאלוג" lang="tl" hreflang="tl" data-title="Distribusyong binomial" data-language-autonym="Tagalog" data-language-local-name="טאגאלוג" class="interlanguage-link-target"><span>Tagalog</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 – טורקית" lang="tr" hreflang="tr" data-title="Binom dağılımı" data-language-autonym="Türkçe" data-language-local-name="טורקית" 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 – אוקראינית" lang="uk" hreflang="uk" data-title="Біноміальний розподіл" data-language-autonym="Українська" data-language-local-name="אוקראינית" 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 – אורדו" lang="ur" hreflang="ur" data-title="دو رقمی توزیع" data-language-autonym="اردو" data-language-local-name="אורדו" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Binomial_taqsimot" title="Binomial taqsimot – אוזבקית" lang="uz" hreflang="uz" data-title="Binomial taqsimot" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="אוזבקית" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</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 – וייטנאמית" lang="vi" hreflang="vi" data-title="Phân phối nhị thức" data-language-autonym="Tiếng Việt" data-language-local-name="וייטנאמית" class="interlanguage-link-target"><span>Tiếng Việt</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 – סינית" lang="zh" hreflang="zh" data-title="二項式分布" data-language-autonym="中文" data-language-local-name="סינית" class="interlanguage-link-target"><span>中文</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 – קנטונזית" lang="yue" hreflang="yue" data-title="二項分佈" data-language-autonym="粵語" data-language-local-name="קנטונזית" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a 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class="new" title="שיחה על דף התוכן (הדף אינו קיים) [t]" accesskey="t"><span>שיחה</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="שינוי הגוון השפה" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">עברית</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> 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class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">כלים</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">העברה לסרגל הצד</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">הסתרה</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="אפשרויות נוספות" > <div class="vector-menu-heading"> פעולות 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href="/w/index.php?title=%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&action=info" title="מידע נוסף על הדף הזה"><span>מידע על הדף</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%A6%D7%99%D7%98%D7%95%D7%98_%D7%93%D7%A3_%D7%96%D7%94&page=%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&id=38186496&wpFormIdentifier=titleform" title="מידע איך לצטט את הדף הזה"><span>ציטוט הדף הזה</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%9E%D7%A7%D7%A6%D7%A8_%D7%9B%D7%AA%D7%95%D7%91%D7%95%D7%AA&url=https%3A%2F%2Fhe.wikipedia.org%2Fwiki%2F%25D7%2594%25D7%25AA%25D7%25A4%25D7%259C%25D7%2592%25D7%2595%25D7%25AA_%25D7%2591%25D7%2599%25D7%25A0%25D7%2595%25D7%259E%25D7%2599%25D7%25AA"><span>קבלת כתובת מקוצרת</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:QrCode&url=https%3A%2F%2Fhe.wikipedia.org%2Fwiki%2F%25D7%2594%25D7%25AA%25D7%25A4%25D7%259C%25D7%2592%25D7%2595%25D7%25AA_%25D7%2591%25D7%2599%25D7%25A0%25D7%2595%25D7%259E%25D7%2599%25D7%25AA"><span>הורדת קוד QR</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> הדפסה/יצוא </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%A1%D7%A4%D7%A8&bookcmd=book_creator&referer=%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"><span>יצירת ספר</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:DownloadAsPdf&page=%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&action=show-download-screen"><span>הורדה כ־PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=%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&printable=yes" title="גרסה להדפסה של הדף הזה [p]" accesskey="p"><span>גרסה להדפסה</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> במיזמים אחרים </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Binomial_distributions" hreflang="en"><span>ויקישיתוף</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem 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data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">מראה</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">העברה לסרגל הצד</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">הסתרה</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">מתוך ויקיפדיה, האנציקלופדיה החופשית</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="he" dir="rtl"><table class="infobox" style="width: 22em; font-size: 95%;"><caption dir="auto" style="background: lightblue; border:1px solid #aaaaaa; border-bottom:0px;">התפלגות בינומית</caption><tbody><tr><td colspan="2" style="background: lightblue; font-size:larger; text-align:center"> <small><b><a href="/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%99%D7%AA_%D7%94%D7%A1%D7%AA%D7%91%D7%A8%D7%95%D7%AA" title="פונקציית הסתברות">פונקציית ההסתברות</a></b></small></td></tr><tr><td colspan="2" style="text-align:center"> <figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/%D7%A7%D7%95%D7%91%D7%A5:Binomial_distribution.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Binomial_distribution.svg/300px-Binomial_distribution.svg.png" decoding="async" width="300" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Binomial_distribution.svg/450px-Binomial_distribution.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Binomial_distribution.svg/600px-Binomial_distribution.svg.png 2x" data-file-width="540" data-file-height="360" /></a><figcaption></figcaption></figure></td></tr><tr><th colspan="2" style="text-align:center;background: lightblue;"> <a href="/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%99%D7%AA_%D7%94%D7%A6%D7%98%D7%91%D7%A8%D7%95%D7%AA" class="mw-redirect" title="פונקציית הצטברות">פונקציית ההסתברות המצטברת</a></th></tr><tr><td colspan="2" style="text-align:center"> <figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/%D7%A7%D7%95%D7%91%D7%A5:Binomial_distribution_cdf.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/Binomial_distribution_cdf.png/300px-Binomial_distribution_cdf.png" decoding="async" width="300" height="225" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/Binomial_distribution_cdf.png/450px-Binomial_distribution_cdf.png 1.5x, //upload.wikimedia.org/wikipedia/commons/5/56/Binomial_distribution_cdf.png 2x" data-file-width="561" data-file-height="420" /></a><figcaption></figcaption></figure></td></tr><tr><th colspan="2" style="text-align:center;background: lightblue;"> מאפיינים</th></tr><tr><th scope="row"> פרמטרים</th><td> p – ההסתברות ל"הצלחה",<br />n – מספר ניסויי ברנולי</td></tr><tr><th scope="row"> <a href="/wiki/%D7%AA%D7%95%D7%9E%D7%9A" class="mw-redirect" title="תומך">תומך</a></th><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 k\in \{0,1,2...,n\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> <mo>∈</mo> <mo fence="false" stretchy="false">{</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>2...</mn> <mo>,</mo> <mi>n</mi> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k\in \{0,1,2...,n\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a31b8f1b7ff5c2fef0ebdb2e9593ee1304dc3ee7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.301ex; height:2.843ex;" alt="{\displaystyle k\in \{0,1,2...,n\}}"></span></td></tr><tr><th scope="row"> <a href="/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%99%D7%AA_%D7%94%D7%A1%D7%AA%D7%91%D7%A8%D7%95%D7%AA" title="פונקציית הסתברות">פונקציית הסתברות</a><br />(pmf)</th><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 \choose k}p^{k}(1-p)^{n-k}\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <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> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {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/b0740476d1ae39255991562d4f8cbfc99cf5e22d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; margin-right: -0.387ex; width:17.409ex; height:6.176ex;" alt="{\displaystyle {n \choose k}p^{k}(1-p)^{n-k}\!}"></span></td></tr><tr><th scope="row"> <a href="/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%99%D7%AA_%D7%94%D7%94%D7%A1%D7%AA%D7%91%D7%A8%D7%95%D7%AA_%D7%94%D7%9E%D7%A6%D7%98%D7%91%D7%A8%D7%AA" class="mw-redirect" title="פונקציית ההסתברות המצטברת">פונקציית ההסתברות המצטברת</a><br />(cdf)</th><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 I_{1-p}(n-\lfloor k\rfloor ,1+\lfloor k\rfloor )\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo>−</mo> <mi>p</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mo fence="false" stretchy="false">⌊</mo> <mi>k</mi> <mo fence="false" stretchy="false">⌋</mo> <mo>,</mo> <mn>1</mn> <mo>+</mo> <mo fence="false" stretchy="false">⌊</mo> <mi>k</mi> <mo fence="false" stretchy="false">⌋</mo> <mo stretchy="false">)</mo> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{1-p}(n-\lfloor k\rfloor ,1+\lfloor k\rfloor )\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/161dc0c96825c9f666660a82d7dd8936f8a096e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.166ex; width:21.595ex; height:3.009ex;" alt="{\displaystyle I_{1-p}(n-\lfloor k\rfloor ,1+\lfloor k\rfloor )\!}"></span></td></tr><tr><th scope="row"> <a href="/wiki/%D7%AA%D7%95%D7%97%D7%9C%D7%AA" title="תוחלת">תוחלת</a></th><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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle np}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d6eb41e0e5e136f594b1a703d2f371d9a5e0c27" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.564ex; height:2.009ex;" alt="{\displaystyle np}"></span></td></tr><tr><th scope="row"> <a href="/wiki/%D7%A1%D7%98%D7%99%D7%99%D7%AA_%D7%AA%D7%A7%D7%9F" title="סטיית תקן">סטיית תקן</a></th><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 {\sqrt {np(1-p)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <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> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {np(1-p)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0dd05a843589c56e7181d231480f1c1c34e2980" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:11.869ex; height:4.843ex;" alt="{\displaystyle {\sqrt {np(1-p)}}}"></span></td></tr><tr><th scope="row"> <a href="/wiki/%D7%97%D7%A6%D7%99%D7%95%D7%9F" title="חציון">חציון</a></th><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 \{\lfloor np\rfloor -1,\lfloor np\rfloor ,\lfloor np\rfloor +1\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <mo fence="false" stretchy="false">⌊</mo> <mi>n</mi> <mi>p</mi> <mo fence="false" stretchy="false">⌋</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mo fence="false" stretchy="false">⌊</mo> <mi>n</mi> <mi>p</mi> <mo fence="false" stretchy="false">⌋</mo> <mo>,</mo> <mo fence="false" stretchy="false">⌊</mo> <mi>n</mi> <mi>p</mi> <mo fence="false" stretchy="false">⌋</mo> <mo>+</mo> <mn>1</mn> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{\lfloor np\rfloor -1,\lfloor np\rfloor ,\lfloor np\rfloor +1\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e1754fa856587a6a37fd1c8bd039c0e4f657f9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:26.285ex; height:2.843ex;" alt="{\displaystyle \{\lfloor np\rfloor -1,\lfloor np\rfloor ,\lfloor np\rfloor +1\}}"></span></td></tr><tr><th scope="row"> <a href="/wiki/%D7%A9%D7%9B%D7%99%D7%97" title="שכיח">ערך שכיח</a></th><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 \lfloor (n+1)\,p\rfloor \!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⌊</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>p</mi> <mo fence="false" stretchy="false">⌋</mo> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lfloor (n+1)\,p\rfloor \!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7785e64fe3b31c98c9be12cd54fb0470607db2fa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.441ex; height:2.843ex;" alt="{\displaystyle \lfloor (n+1)\,p\rfloor \!}"></span></td></tr><tr><th scope="row"> <a href="/wiki/%D7%A9%D7%95%D7%A0%D7%95%D7%AA" title="שונות">שונות</a></th><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)}"> <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> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle np(1-p)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57f093250a1d822df677a03ac8aa78c6a8029866" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.546ex; height:2.843ex;" alt="{\displaystyle np(1-p)}"></span></td></tr><tr><th scope="row"> <a href="/wiki/%D7%90%D7%A0%D7%98%D7%A8%D7%95%D7%A4%D7%99%D7%94_(%D7%A1%D7%98%D7%98%D7%99%D7%A1%D7%98%D7%99%D7%A7%D7%94)" title="אנטרופיה (סטטיסטיקה)">אנטרופיה</a></th><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 {\frac {1}{2}}\ln \left(2\pi e\ np(1-p)\right)+O\left({\frac {1}{n}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ln</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>π</mi> <mi>e</mi> <mtext> </mtext> <mi>n</mi> <mi>p</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>p</mi> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mi>O</mi> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{2}}\ln \left(2\pi e\ np(1-p)\right)+O\left({\frac {1}{n}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9ccf16f92fb5b417bc04df5ecc170c99abcb15a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:30.491ex; height:6.176ex;" alt="{\displaystyle {\frac {1}{2}}\ln \left(2\pi e\ np(1-p)\right)+O\left({\frac {1}{n}}\right)}"></span></td></tr><tr><th scope="row"> <a href="/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%94_%D7%99%D7%95%D7%A6%D7%A8%D7%AA_%D7%9E%D7%95%D7%9E%D7%A0%D7%98%D7%99%D7%9D" title="פונקציה יוצרת מומנטים">פונקציה יוצרת מומנטים</a><br />(mgf)</th><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 (1-p+pe^{t})^{n}\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>p</mi> <mo>+</mo> <mi>p</mi> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (1-p+pe^{t})^{n}\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78281138a2f0dc4c3c3fd7e09ab301ddfced12af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:14.119ex; height:3.009ex;" alt="{\displaystyle (1-p+pe^{t})^{n}\!}"></span></td></tr><tr><th scope="row"> <a href="/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%94_%D7%90%D7%95%D7%A4%D7%99%D7%99%D7%A0%D7%99%D7%AA_(%D7%94%D7%A1%D7%AA%D7%91%D7%A8%D7%95%D7%AA)" title="פונקציה אופיינית (הסתברות)">פונקציה אופיינית</a></th><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 (1-p+pe^{it})^{n}\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>p</mi> <mo>+</mo> <mi>p</mi> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>t</mi> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (1-p+pe^{it})^{n}\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/694fc03c54e5edadb01370457e0b09a37e8310e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:14.687ex; height:3.176ex;" alt="{\displaystyle (1-p+pe^{it})^{n}\!}"></span></td></tr><tr><th scope="row"> <a href="/wiki/%D7%A6%D7%99%D7%93%D7%95%D7%93_(%D7%A1%D7%98%D7%98%D7%99%D7%A1%D7%98%D7%99%D7%A7%D7%94)" title="צידוד (סטטיסטיקה)">צידוד</a></th><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 {\frac {1-2p}{\sqrt {np(1-p)}}}\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>−</mo> <mn>2</mn> <mi>p</mi> </mrow> <msqrt> <mi>n</mi> <mi>p</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>p</mi> <mo stretchy="false">)</mo> </msqrt> </mfrac> </mrow> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1-2p}{\sqrt {np(1-p)}}}\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b56fdab3aed963fc543720e4cc7ddb639938d3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; margin-right: -0.108ex; width:12.427ex; height:6.676ex;" alt="{\displaystyle {\frac {1-2p}{\sqrt {np(1-p)}}}\!}"></span></td></tr><tr><th scope="row"> <a href="/wiki/%D7%92%D7%91%D7%A0%D7%95%D7%A0%D7%99%D7%95%D7%AA_(%D7%A1%D7%98%D7%98%D7%99%D7%A1%D7%98%D7%99%D7%A7%D7%94)" title="גבנוניות (סטטיסטיקה)">גבנוניות</a></th><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 {\frac {1-6p(1-p)}{np(1-p)}}\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>−</mo> <mn>6</mn> <mi>p</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>p</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>n</mi> <mi>p</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>p</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1-6p(1-p)}{np(1-p)}}\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/02b066e0d7efaec08be094fd2a92b02c7aa00f0c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; margin-right: -0.108ex; width:13.874ex; height:6.509ex;" alt="{\displaystyle {\frac {1-6p(1-p)}{np(1-p)}}\!}"></span></td></tr></tbody></table> <p><b>התפלגות בינומית</b> היא <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%91%D7%93%D7%99%D7%93%D7%94" title="התפלגות בדידה">התפלגות בדידה</a>, המתארת את מספר ההצלחות בסדרה של <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> <a href="/wiki/%D7%A0%D7%99%D7%A1%D7%95%D7%99%D7%99_%D7%91%D7%A8%D7%A0%D7%95%D7%9C%D7%99" class="mw-redirect" title="ניסויי ברנולי">ניסויי ברנולי</a> בלתי תלויים עם <a href="/wiki/%D7%94%D7%A1%D7%AA%D7%91%D7%A8%D7%95%D7%AA" title="הסתברות">הסתברות</a> הצלחה <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> בכל אחד. אם <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> <a href="/wiki/%D7%9E%D7%A9%D7%AA%D7%A0%D7%94_%D7%9E%D7%A7%D7%A8%D7%99" title="משתנה מקרי">משתנה מקרי</a> בינומי המתאים לסדרת ניסויים שכזו מסמנים <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\sim \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\sim \mathrm {Bin} (n,p)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bca3b7938212164e1ab6ca3e5596b8e8c17919e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.071ex; height:2.843ex;" alt="{\displaystyle X\sim \mathrm {Bin} (n,p)}"></span>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="ההתפלגות_הבינומית"><span id=".D7.94.D7.94.D7.AA.D7.A4.D7.9C.D7.92.D7.95.D7.AA_.D7.94.D7.91.D7.99.D7.A0.D7.95.D7.9E.D7.99.D7.AA"></span>ההתפלגות הבינומית</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%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&action=edit&section=1" title="עריכת קוד המקור של הפרק: ההתפלגות הבינומית"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%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&veaction=edit&section=1" title="עריכת פסקה: "ההתפלגות הבינומית"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>ההתפלגות של משתנה בינומי <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\sim \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\sim \mathrm {Bin} (n,p)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bca3b7938212164e1ab6ca3e5596b8e8c17919e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.071ex; height:2.843ex;" alt="{\displaystyle X\sim \mathrm {Bin} (n,p)}"></span> היא </p><p><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)=\Pr \left(X=k\right)={\binom {n}{k}}p^{k}q^{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> <mo movablelimits="true" form="prefix">Pr</mo> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo>=</mo> <mi>k</mi> </mrow> <mo>)</mo> </mrow> <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> <msup> <mi>q</mi> <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)=\Pr \left(X=k\right)={\binom {n}{k}}p^{k}q^{n-k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/91555d6119577ba2eba079ef4447a49b5d35021e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; margin-left: -0.089ex; width:34.596ex; height:6.176ex;" alt="{\displaystyle p_{X}(k)=\Pr \left(X=k\right)={\binom {n}{k}}p^{k}q^{n-k}}"></span> </p><p>עבור <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 k=0,1,\ldots ,n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k=0,1,\ldots ,n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff8f0e25dbb29fa50f2c902ff315cb452daf54c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.241ex; height:2.509ex;" alt="{\displaystyle k=0,1,\ldots ,n}"></span>, ונהוג לסמן את ההסתברות לכישלון בניסוי בודד <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 q=1-p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>q</mi> <mo>=</mo> <mn>1</mn> <mo>−</mo> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q=1-p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/22e387fe24ba3da5f9a0dc424923cdfc2c08990c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.34ex; height:2.509ex;" alt="{\displaystyle q=1-p}"></span>. הסימון <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 {\binom {n}{k}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <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> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\binom {n}{k}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/963a810ba39e3e0725c523d0c98b18f39786ebb2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:4.816ex; height:6.176ex;" alt="{\displaystyle {\binom {n}{k}}}"></span> מתייחס ל<a href="/wiki/%D7%9E%D7%A7%D7%93%D7%9D_%D7%91%D7%99%D7%A0%D7%95%D7%9E%D7%99" title="מקדם בינומי">מקדם הבינומי</a>, שממנו קיבלה ההתפלגות את שמה. </p><p>אכן, ההסתברות להצליח בדיוק <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 k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}"></span> פעמים בסדרה של <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> ניסויי ברנולי עם פרמטר הצלחה <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> שווה לסכום ההסתברויות של כל הסדרות האפשריות של תוצאות שיש בהן <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 k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}"></span> הצלחות ו-<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-k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>−</mo> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n-k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b98e1d6a69bccd09a4b9b69bdf03a08c1706c8c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.446ex; height:2.343ex;" alt="{\displaystyle n-k}"></span> כישלונות. מכיוון שהניסויים בלתי תלויים, הסיכוי של סדרה מסוימת (כגון הצלחה-הצלחה-כישלון-כישלון-הצלחה) שווה למכפלה <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^{k}q^{n-k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msup> <msup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mi>k</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p^{k}q^{n-k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fdc753d91d7f60060c02fdac9b5f37924901c847" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:6.78ex; height:3.009ex;" alt="{\displaystyle p^{k}q^{n-k}}"></span>. לכן ההסתברות הכוללת שווה למספר הדרכים לבחור את <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 k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}"></span> הניסויים המוצלחים מתוך כלל <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> הניסויים, שהוא ה<a href="/wiki/%D7%9E%D7%A7%D7%93%D7%9D_%D7%91%D7%99%D7%A0%D7%95%D7%9E%D7%99" title="מקדם בינומי">מקדם הבינומי</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 {\binom {n}{k}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <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> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\binom {n}{k}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/963a810ba39e3e0725c523d0c98b18f39786ebb2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:4.816ex; height:6.176ex;" alt="{\displaystyle {\binom {n}{k}}}"></span>, כפול <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^{k}q^{n-k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msup> <msup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mi>k</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p^{k}q^{n-k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fdc753d91d7f60060c02fdac9b5f37924901c847" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:6.78ex; height:3.009ex;" alt="{\displaystyle p^{k}q^{n-k}}"></span>. </p> <div class="mw-heading mw-heading3"><h3 id="סכום_ההסתברויות"><span id=".D7.A1.D7.9B.D7.95.D7.9D_.D7.94.D7.94.D7.A1.D7.AA.D7.91.D7.A8.D7.95.D7.99.D7.95.D7.AA"></span>סכום ההסתברויות</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%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&action=edit&section=2" title="עריכת קוד המקור של הפרק: סכום ההסתברויות"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%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&veaction=edit&section=2" title="עריכת פסקה: "סכום ההסתברויות"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>כמו בכל התפלגות, סכום ההסתברויות לכל התוצאות האפשריות הוא 1. אפשר לסכם את ההסתברויות ישירות על ידי <a href="/wiki/%D7%A0%D7%95%D7%A1%D7%97%D7%AA_%D7%94%D7%91%D7%99%D7%A0%D7%95%D7%9D" class="mw-redirect" title="נוסחת הבינום">נוסחת הבינום</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 \sum _{k=0}^{n}{n \choose k}p^{k}q^{n-k}=(p+q)^{n}=1^{n}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <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> <msup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mi>k</mi> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <mi>p</mi> <mo>+</mo> <mi>q</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>=</mo> <msup> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{k=0}^{n}{n \choose k}p^{k}q^{n-k}=(p+q)^{n}=1^{n}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ab6b357c6fd73c4aa5fcba14daf9483d552eeee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:36.195ex; height:7.009ex;" alt="{\displaystyle \sum _{k=0}^{n}{n \choose k}p^{k}q^{n-k}=(p+q)^{n}=1^{n}=1}"></span>. </p> <div class="mw-heading mw-heading3"><h3 id="תוחלת_ושונות"><span id=".D7.AA.D7.95.D7.97.D7.9C.D7.AA_.D7.95.D7.A9.D7.95.D7.A0.D7.95.D7.AA"></span>תוחלת ושונות</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%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&action=edit&section=3" title="עריכת קוד המקור של הפרק: תוחלת ושונות"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%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&veaction=edit&section=3" title="עריכת פסקה: "תוחלת ושונות"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>ה<a href="/wiki/%D7%AA%D7%95%D7%97%D7%9C%D7%AA" title="תוחלת">תוחלת</a> של משתנה מקרי בינומי היא <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle np}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d6eb41e0e5e136f594b1a703d2f371d9a5e0c27" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.564ex; height:2.009ex;" alt="{\displaystyle np}"></span>, וה<a href="/wiki/%D7%A9%D7%95%D7%A0%D7%95%D7%AA" title="שונות">שונות</a> שלו היא <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 npq}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mi>p</mi> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle npq}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de73b886a834b8ba9d92dbb5419b13c6aab2a48e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.634ex; height:2.009ex;" alt="{\displaystyle npq}"></span>. </p> <div class="mw-heading mw-heading2"><h2 id="דוגמה"><span id=".D7.93.D7.95.D7.92.D7.9E.D7.94"></span>דוגמה</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%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&action=edit&section=4" title="עריכת קוד המקור של הפרק: דוגמה"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%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&veaction=edit&section=4" title="עריכת פסקה: "דוגמה"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>מטילים <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 7}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>7</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 7}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee716ec61382a6b795092c0edd859d12e64cbba8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 7}"></span> פעמים מטבע בעל סיכוי ל"עץ" של <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 0.6}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0.6</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0.6}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c0001ac9c2a3bfc0abcfa25e7375e7bc62f5a15" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.972ex; height:2.176ex;" alt="{\displaystyle 0.6}"></span>. נניח שההטלות הן בלתי תלויות זו בזו. אם נסמן את מספר הפעמים בהן התקבל "עץ" ב-<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> אז <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\sim \mathrm {Bin} (7,0.6)}"> <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> <mn>7</mn> <mo>,</mo> <mn>0.6</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X\sim \mathrm {Bin} (7,0.6)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82df1145eaaa3d5d073a2004fa8023e0c53fa1ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.641ex; height:2.843ex;" alt="{\displaystyle X\sim \mathrm {Bin} (7,0.6)}"></span>. ההסתברות לקבלת "עץ" <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 4}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>4</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 4}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/295b4bf1de7cd3500e740e0f4f0635db22d87b42" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 4}"></span> פעמים בדיוק היא <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 \Pr(X=4)={\binom {7}{4}}\cdot 0.6^{4}\cdot 0.4^{3}=0.290304}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo movablelimits="true" form="prefix">Pr</mo> <mo stretchy="false">(</mo> <mi>X</mi> <mo>=</mo> <mn>4</mn> <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"> <mn>7</mn> <mn>4</mn> </mfrac> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">)</mo> </mrow> </mrow> </mrow> <mo>⋅</mo> <msup> <mn>0.6</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>⋅</mo> <msup> <mn>0.4</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>=</mo> <mn>0.290304</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Pr(X=4)={\binom {7}{4}}\cdot 0.6^{4}\cdot 0.4^{3}=0.290304}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2add61f5e44a1395abaef0a253686842e2f73bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:41.519ex; height:6.176ex;" alt="{\displaystyle \Pr(X=4)={\binom {7}{4}}\cdot 0.6^{4}\cdot 0.4^{3}=0.290304}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="התפלגות_בינומית_שלילית"><span id=".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_.D7.A9.D7.9C.D7.99.D7.9C.D7.99.D7.AA"></span>התפלגות בינומית שלילית</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%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&action=edit&section=5" title="עריכת קוד המקור של הפרק: התפלגות בינומית שלילית"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%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&veaction=edit&section=5" title="עריכת פסקה: "התפלגות בינומית שלילית"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Postscript-viewer-blue.svg/25px-Postscript-viewer-blue.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Postscript-viewer-blue.svg/38px-Postscript-viewer-blue.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Postscript-viewer-blue.svg/50px-Postscript-viewer-blue.svg.png 2x" data-file-width="60" data-file-height="60" /></span></span> ערך מורחב – <b><a href="/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_%D7%A9%D7%9C%D7%99%D7%9C%D7%99%D7%AA" title="התפלגות בינומית שלילית">התפלגות בינומית שלילית</a></b><br /></dd></dl> <p>נאמר שמשתנה מקרי <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> מתפלג בינומית שלילית עם פרמטרים <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 (r,p)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>r</mi> <mo>,</mo> <mi>p</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (r,p)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e586c8bcfdafc9bfbc7464486e27b4c643b5f14" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.061ex; height:2.843ex;" alt="{\displaystyle (r,p)}"></span> אם </p><p><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)={\frac {\Gamma (r+k)}{k!\cdot \Gamma (r)}}p^{r}(1-p)^{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> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Γ</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo>+</mo> <mi>k</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>k</mi> <mo>!</mo> <mo>⋅</mo> <mi mathvariant="normal">Γ</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</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>k</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{X}(k)={\frac {\Gamma (r+k)}{k!\cdot \Gamma (r)}}p^{r}(1-p)^{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7a48f22effcf3e3e7f8a7505e133860767b67d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; margin-left: -0.089ex; width:28.422ex; height:6.509ex;" alt="{\displaystyle p_{X}(k)={\frac {\Gamma (r+k)}{k!\cdot \Gamma (r)}}p^{r}(1-p)^{k}}"></span> </p><p>כאשר <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 \Gamma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Γ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Gamma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4cfde86a3f7ec967af9955d0988592f0693d2b19" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.453ex; height:2.176ex;" alt="{\displaystyle \Gamma }"></span> היא <a href="/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%99%D7%AA_%D7%92%D7%9E%D7%90" title="פונקציית גמא">פונקציית גמא</a> המרחיבה את מושג ה<a href="/wiki/%D7%A2%D7%A6%D7%A8%D7%AA_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="עצרת (מתמטיקה)">עצרת</a> אל <a href="/wiki/%D7%94%D7%9E%D7%99%D7%A9%D7%95%D7%A8_%D7%94%D7%9E%D7%A8%D7%95%D7%9B%D7%91" title="המישור המרוכב">המישור המרוכב</a>. </p> <div class="mw-heading mw-heading2"><h2 id="קשרים_להתפלגויות_אחרות"><span id=".D7.A7.D7.A9.D7.A8.D7.99.D7.9D_.D7.9C.D7.94.D7.AA.D7.A4.D7.9C.D7.92.D7.95.D7.99.D7.95.D7.AA_.D7.90.D7.97.D7.A8.D7.95.D7.AA"></span>קשרים להתפלגויות אחרות</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%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&action=edit&section=6" title="עריכת קוד המקור של הפרק: קשרים להתפלגויות אחרות"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%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&veaction=edit&section=6" title="עריכת פסקה: "קשרים להתפלגויות אחרות"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="סכום_של_משתנים_מקריים_בינומיים"><span id=".D7.A1.D7.9B.D7.95.D7.9D_.D7.A9.D7.9C_.D7.9E.D7.A9.D7.AA.D7.A0.D7.99.D7.9D_.D7.9E.D7.A7.D7.A8.D7.99.D7.99.D7.9D_.D7.91.D7.99.D7.A0.D7.95.D7.9E.D7.99.D7.99.D7.9D"></span>סכום של משתנים מקריים בינומיים</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%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&action=edit&section=7" title="עריכת קוד המקור של הפרק: סכום של משתנים מקריים בינומיים"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%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&veaction=edit&section=7" title="עריכת פסקה: "סכום של משתנים מקריים בינומיים"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>אם <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\sim \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\sim \mathrm {Bin} (n,p)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bca3b7938212164e1ab6ca3e5596b8e8c17919e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.071ex; height:2.843ex;" alt="{\displaystyle X\sim \mathrm {Bin} (n,p)}"></span> וכן <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 Y\sim \mathrm {Bin} (m,p)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</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>m</mi> <mo>,</mo> <mi>p</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y\sim \mathrm {Bin} (m,p)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/15c4f46236464511fe3e54f9c6fedd37b7112fce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.51ex; height:2.843ex;" alt="{\displaystyle Y\sim \mathrm {Bin} (m,p)}"></span> הם שני <a href="/wiki/%D7%90%D7%99_%D7%AA%D7%9C%D7%95%D7%AA_(%D7%A1%D7%98%D7%98%D7%99%D7%A1%D7%98%D7%99%D7%A7%D7%94)" class="mw-redirect" title="אי תלות (סטטיסטיקה)">משתנים מקריים בלתי תלויים</a>, בעלי אותו פרמטר הצלחה <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> אז <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+Y\sim \mathrm {Bin} (n+m,p)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> <mo>+</mo> <mi>Y</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>m</mi> <mo>,</mo> <mi>p</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X+Y\sim \mathrm {Bin} (n+m,p)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7c66ed100c660f7cb7f5e1009320cfb2edd0e4b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:23.565ex; height:2.843ex;" alt="{\displaystyle X+Y\sim \mathrm {Bin} (n+m,p)}"></span>, זאת אומרת סכומם של המשתנים המקריים גם כן מתפלג בינומי. </p> <div class="mw-heading mw-heading3"><h3 id="התפלגות_ברנולי"><span id=".D7.94.D7.AA.D7.A4.D7.9C.D7.92.D7.95.D7.AA_.D7.91.D7.A8.D7.A0.D7.95.D7.9C.D7.99"></span>התפלגות ברנולי</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%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&action=edit&section=8" title="עריכת קוד המקור של הפרק: התפלגות ברנולי"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%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&veaction=edit&section=8" title="עריכת פסקה: "התפלגות ברנולי"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%91%D7%A8%D7%A0%D7%95%D7%9C%D7%99" title="התפלגות ברנולי">התפלגות ברנולי</a> היא <a href="/wiki/%D7%9E%D7%A7%D7%A8%D7%94_%D7%A4%D7%A8%D7%98%D7%99" title="מקרה פרטי">מקרה פרטי</a> של התפלגות בינומית כאשר <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\sim \mathrm {Bin} (1,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> <mn>1</mn> <mo>,</mo> <mi>p</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X\sim \mathrm {Bin} (1,p)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/804d5149373e005ac9a97062e88f477c3fb3b4c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.839ex; height:2.843ex;" alt="{\displaystyle X\sim \mathrm {Bin} (1,p)}"></span> ונהוג לסמן <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\sim \mathrm {Ber} (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">e</mi> <mi mathvariant="normal">r</mi> </mrow> <mo stretchy="false">(</mo> <mi>p</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X\sim \mathrm {Ber} (p)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2fa5b011888eb2dd80b5861438be82244bf50ce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.647ex; height:2.843ex;" alt="{\displaystyle X\sim \mathrm {Ber} (p)}"></span>. למעשה, ניתן לראות בכל התפלגות בינומית Bin(<i>n</i>, <i>p</i>) כסכום של <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> <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA" title="התפלגות">התפלגויות</a> ברנולי בלתי תלויות שלכולן אותה הסתברות <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>. </p> <div class="mw-heading mw-heading3"><h3 id="קירוב_על_ידי_התפלגות_פואסון"><span id=".D7.A7.D7.99.D7.A8.D7.95.D7.91_.D7.A2.D7.9C_.D7.99.D7.93.D7.99_.D7.94.D7.AA.D7.A4.D7.9C.D7.92.D7.95.D7.AA_.D7.A4.D7.95.D7.90.D7.A1.D7.95.D7.9F"></span>קירוב על ידי התפלגות פואסון</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%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&action=edit&section=9" title="עריכת קוד המקור של הפרק: קירוב על ידי התפלגות פואסון"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%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&veaction=edit&section=9" title="עריכת פסקה: "קירוב על ידי התפלגות פואסון"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>ניתן למצוא קירוב להתפלגות הבינומית עבור ערכי <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> גדולים מאוד וערכי <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> קטנים מאוד על ידי שימוש ב<a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%A4%D7%95%D7%90%D7%A1%D7%95%D7%9F" title="התפלגות פואסון">התפלגות פואסון</a> עם פרמטר <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 \lambda =np}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mo>=</mo> <mi>n</mi> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda =np}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a42ff2cb62b86d1ecc7b806cd8b32829a8a5f3a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.018ex; height:2.509ex;" alt="{\displaystyle \lambda =np}"></span>. באופן פורמלי, אם <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_{n}\}_{n=1}^{\infty }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <msubsup> <mo fence="false" stretchy="false">}</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{X_{n}\}_{n=1}^{\infty }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3dbb8ecc0e41cc2b7a0cf789d3c6f800362f5430" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.787ex; height:3.009ex;" alt="{\displaystyle \{X_{n}\}_{n=1}^{\infty }}"></span> סדרת משתנים מקריים המתפלגים <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_{n}\sim \mathrm {Bin} \left(n,{\frac {\lambda }{n}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>∼</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> </mrow> <mrow> <mo>(</mo> <mrow> <mi>n</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mi>n</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{n}\sim \mathrm {Bin} \left(n,{\frac {\lambda }{n}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2dfb860d1a7f3a99bce9453af50b6598d0187542" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:18.294ex; height:6.176ex;" alt="{\displaystyle X_{n}\sim \mathrm {Bin} \left(n,{\frac {\lambda }{n}}\right)}"></span> אז <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 \lim _{n\to \infty }\Pr(X=k)=\Pr(Y=k)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mo movablelimits="true" form="prefix">Pr</mo> <mo stretchy="false">(</mo> <mi>X</mi> <mo>=</mo> <mi>k</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo movablelimits="true" form="prefix">Pr</mo> <mo stretchy="false">(</mo> <mi>Y</mi> <mo>=</mo> <mi>k</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{n\to \infty }\Pr(X=k)=\Pr(Y=k)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bf34f9e9554f635e5210d421397dd2ca038ed22" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:28.738ex; height:3.843ex;" alt="{\displaystyle \lim _{n\to \infty }\Pr(X=k)=\Pr(Y=k)}"></span> כאשר <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 Y\sim \mathrm {Pois} (\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> <mo>∼</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">s</mi> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y\sim \mathrm {Pois} (\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a27505512a7cd7c2a91c86cabe1542bb1d1bbb3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.345ex; height:2.843ex;" alt="{\displaystyle Y\sim \mathrm {Pois} (\lambda )}"></span>. </p> <div class="mw-heading mw-heading3"><h3 id="קירוב_על_ידי_התפלגות_נורמלית"><span id=".D7.A7.D7.99.D7.A8.D7.95.D7.91_.D7.A2.D7.9C_.D7.99.D7.93.D7.99_.D7.94.D7.AA.D7.A4.D7.9C.D7.92.D7.95.D7.AA_.D7.A0.D7.95.D7.A8.D7.9E.D7.9C.D7.99.D7.AA"></span>קירוב על ידי התפלגות נורמלית</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%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&action=edit&section=10" title="עריכת קוד המקור של הפרק: קירוב על ידי התפלגות נורמלית"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%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&veaction=edit&section=10" title="עריכת פסקה: "קירוב על ידי התפלגות נורמלית"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>אם <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> <a href="/wiki/%D7%92%D7%93%D7%95%D7%9C_%D7%9E%D7%A1%D7%A4%D7%99%D7%A7" title="גדול מספיק">גדול מספיק</a> חוסר הסימטריה שבהתפלגות לא יהיה גדול, במקרה זה נוכל לקרב את ההתפלגות הבינומית על ידי <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%A0%D7%95%D7%A8%D7%9E%D7%9C%D7%99%D7%AA" title="התפלגות נורמלית">ההתפלגות הנורמלית</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 X\sim N(np,np(1-p))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> <mo>∼</mo> <mi>N</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mi>p</mi> <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 stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X\sim N(np,np(1-p))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebf7302be5f17b8c312b34fdda7a818353a5bbde" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.095ex; height:2.843ex;" alt="{\displaystyle X\sim N(np,np(1-p))}"></span>. כשמשתמשים בהתפלגות הנורמלית על מנת לקרב התפלגות בינומית, נהוג להשתמש ב<a href="/wiki/%D7%AA%D7%99%D7%A7%D7%95%D7%9F_%D7%A8%D7%A6%D7%99%D7%A4%D7%95%D7%AA" title="תיקון רציפות">תיקון רציפות</a> על מנת לשפר את איכות הקירוב. </p> <div class="mw-heading mw-heading2"><h2 id="התפלגויות_קשורות"><span id=".D7.94.D7.AA.D7.A4.D7.9C.D7.92.D7.95.D7.99.D7.95.D7.AA_.D7.A7.D7.A9.D7.95.D7.A8.D7.95.D7.AA"></span>התפלגויות קשורות</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%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&action=edit&section=11" title="עריכת קוד המקור של הפרק: התפלגויות קשורות"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%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&veaction=edit&section=11" title="עריכת פסקה: "התפלגויות קשורות"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <tbody><tr> <th></th> <th>עם החזרה</th> <th>בלי החזרה </th></tr> <tr> <td>מספר הצלחות מתוך מספר הוצאות</td> <td>התפלגות בינומית</td> <td><a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%94%D7%99%D7%A4%D7%A8%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%AA" title="התפלגות היפרגאומטרית">התפלגות היפרגאומטרית</a> </td></tr> <tr> <td>מספר הוצאות עד מספר הצלחות</td> <td><a href="/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_%D7%A9%D7%9C%D7%99%D7%9C%D7%99%D7%AA" title="התפלגות בינומית שלילית">התפלגות בינומית שלילית</a></td> <td><a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%94%D7%99%D7%A4%D7%A8%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%AA_%D7%A9%D7%9C%D7%99%D7%9C%D7%99%D7%AA" title="התפלגות היפרגאומטרית שלילית">התפלגות היפרגאומטרית שלילית</a> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="ראו_גם"><span id=".D7.A8.D7.90.D7.95_.D7.92.D7.9D"></span>ראו גם</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%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&action=edit&section=12" title="עריכת קוד המקור של הפרק: ראו גם"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%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&veaction=edit&section=12" title="עריכת פסקה: "ראו גם"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%D7%AA%D7%99%D7%91%D7%AA_%D7%92%D7%9C%D7%98%D7%95%D7%9F" title="תיבת גלטון">תיבת גלטון</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="קישורים_חיצוניים"><span id=".D7.A7.D7.99.D7.A9.D7.95.D7.A8.D7.99.D7.9D_.D7.97.D7.99.D7.A6.D7.95.D7.A0.D7.99.D7.99.D7.9D"></span>קישורים חיצוניים</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%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&action=edit&section=13" title="עריכת קוד המקור של הפרק: קישורים חיצוניים"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%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&veaction=edit&section=13" title="עריכת פסקה: "קישורים חיצוניים"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="sistersitebox plainlinks noprint" style="margin: 0 1em 0.5em 0;float: left;"><tbody><tr><th style="text-align:center">מיזמי <a href="/wiki/%D7%A7%D7%A8%D7%9F_%D7%95%D7%99%D7%A7%D7%99%D7%9E%D7%93%D7%99%D7%94" title="קרן ויקימדיה">קרן ויקימדיה</a></th></tr><tr><td><div class="sisterwikilinkT"><span typeof="mw:File"><span title="ויקיספר"><img alt="ויקיספר" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/20px-Wikibooks-logo.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/30px-Wikibooks-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/40px-Wikibooks-logo.svg.png 2x" data-file-width="300" data-file-height="300" /></span></span> ספר לימוד בוויקיספר: <b><a href="https://he.wikibooks.org/wiki/%D7%94%D7%A1%D7%AA%D7%91%D7%A8%D7%95%D7%AA/%D7%9E%D7%A9%D7%AA%D7%A0%D7%99%D7%9D_%D7%9E%D7%A7%D7%A8%D7%99%D7%99%D7%9D/%D7%9E%D7%A9%D7%AA%D7%A0%D7%99%D7%9D_%D7%9E%D7%A7%D7%A8%D7%99%D7%99%D7%9D_%D7%91%D7%93%D7%99%D7%93%D7%99%D7%9D/%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" class="extiw" title="b:הסתברות/משתנים מקריים/משתנים מקריים בדידים/התפלגות בינומית">הסתברות/משתנים מקריים/משתנים מקריים בדידים/התפלגות בינומית</a></b></div></td></tr><tr><td><div class="sisterwikilinkT"><span typeof="mw:File"><span title="ויקישיתוף"><img alt="ויקישיתוף" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/20px-Commons-logo.svg.png" decoding="async" width="20" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/40px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> תמונות ומדיה בוויקישיתוף: <b><a href="https://commons.wikimedia.org/wiki/Category:Binomial_distributions" class="extiw" title="commons:Category:Binomial distributions">התפלגות בינומית</a></b></div></td></tr></tbody></table><style data-mw-deduplicate="TemplateStyles:r36773993">.mw-parser-output .sistersitebox{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:#f9f9f9}</style> <ul><li><a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/BinomialDistribution.html">התפלגות בינומית</a>, באתר <a href="/wiki/MathWorld" title="MathWorld">MathWorld</a> <span dir="rtl" class="languageicon">(באנגלית)</span><style data-mw-deduplicate="TemplateStyles:r36549940">.mw-parser-output .languageicon{font-size:0.95em;font-weight:bold;color:#555}</style></li> <li><a rel="nofollow" class="external text" href="https://www.britannica.com/topic/binomial-distribution">התפלגות בינומית</a>, באתר <a href="/wiki/%D7%90%D7%A0%D7%A6%D7%99%D7%A7%D7%9C%D7%95%D7%A4%D7%93%D7%99%D7%94_%D7%91%D7%A8%D7%99%D7%98%D7%A0%D7%99%D7%A7%D7%94" title="אנציקלופדיה בריטניקה">אנציקלופדיה בריטניקה</a> <span dir="rtl" class="languageicon">(באנגלית)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r36549940"></li></ul> <p><br /> </p> <table class="navbox nowraplinks" style="width: 90%; clear: both; margin: 0.5em auto; margin-top: 0.5em; margin-bottom: 0.5em; padding: 0.2em; text-align: right;"> <tbody><tr> <th colspan="3" style="text-align: center; padding-top: 0.1em; padding-bottom: 0.1em; color: black; background:#d1eeee; font-weight: bold;"><a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA" title="התפלגות">התפלגויות</a> </th></tr> <tr> <td style="background-color: #F2F3F4; text-align: right; font-weight: bold; padding-left: 5px;"><a href="/wiki/%D7%A7%D7%98%D7%92%D7%95%D7%A8%D7%99%D7%94:%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%99%D7%95%D7%AA_%D7%91%D7%93%D7%99%D7%93%D7%95%D7%AA" title="קטגוריה:התפלגויות בדידות">התפלגויות בדידות כלליות</a> </td> <td style="padding-right: 5px; text-align: right;"><a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%90%D7%97%D7%99%D7%93%D7%94_%D7%91%D7%93%D7%99%D7%93%D7%94" title="התפלגות אחידה בדידה">אחידה בדידה</a> • <a class="mw-selflink selflink">בינומית</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%9E%D7%95%D7%9C%D7%98%D7%99%D7%A0%D7%95%D7%9E%D7%99%D7%AA" title="התפלגות מולטינומית">מולטינומית</a> • <a href="/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_%D7%A9%D7%9C%D7%99%D7%9C%D7%99%D7%AA" title="התפלגות בינומית שלילית">בינומית שלילית</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%91%D7%A8%D7%A0%D7%95%D7%9C%D7%99" title="התפלגות ברנולי">ברנולי</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%AA" title="התפלגות גאומטרית">גאומטרית</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%94%D7%99%D7%A4%D7%A8%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%AA" title="התפלגות היפרגאומטרית">היפרגאומטרית</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%94%D7%99%D7%A4%D7%A8%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%AA_%D7%A9%D7%9C%D7%99%D7%9C%D7%99%D7%AA" title="התפלגות היפרגאומטרית שלילית">היפרגאומטרית שלילית</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%9E%D7%A0%D7%95%D7%95%D7%A0%D7%AA" title="התפלגות מנוונת">מנוונת</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%A4%D7%95%D7%90%D7%A1%D7%95%D7%9F" title="התפלגות פואסון">פואסון</a> </td> <td rowspan="5" align="center" style="text-align: center; vertical-align: middle;"><figure class="mw-halign-left" typeof="mw:File"><a href="/wiki/%D7%A7%D7%95%D7%91%D7%A5:Normal_distribution_pdf.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Normal_distribution_pdf.png/120px-Normal_distribution_pdf.png" decoding="async" width="120" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Normal_distribution_pdf.png/180px-Normal_distribution_pdf.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Normal_distribution_pdf.png/240px-Normal_distribution_pdf.png 2x" data-file-width="1300" data-file-height="975" /></a><figcaption></figcaption></figure> </td></tr> <tr> <td style="background-color: #F2F3F4; text-align: right; font-weight: bold; padding-left: 5px;"><a href="/wiki/%D7%A7%D7%98%D7%92%D7%95%D7%A8%D7%99%D7%94:%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%99%D7%95%D7%AA_%D7%A8%D7%A6%D7%99%D7%A4%D7%95%D7%AA" title="קטגוריה:התפלגויות רציפות">התפלגויות רציפות כלליות</a> </td> <td style="padding-right: 5px; text-align: right;"><a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%90%D7%97%D7%99%D7%93%D7%94_%D7%A8%D7%A6%D7%99%D7%A4%D7%94" title="התפלגות אחידה רציפה">אחידה רציפה</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%91%D7%98%D7%90" title="התפלגות בטא">בטא</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%92%D7%9E%D7%90" title="התפלגות גמא">גמא</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%9C%D7%95%D7%92-%D7%A0%D7%95%D7%A8%D7%9E%D7%9C%D7%99%D7%AA" title="התפלגות לוג-נורמלית">לוג-נורמלית</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%9E%D7%A2%D7%A8%D7%99%D7%9B%D7%99%D7%AA" title="התפלגות מעריכית">מעריכית (אקספוננציאלית)</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%A0%D7%95%D7%A8%D7%9E%D7%9C%D7%99%D7%AA" title="התפלגות נורמלית">נורמלית (גאוסית)</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%9C%D7%A4%D7%9C%D7%A1" title="התפלגות לפלס">לפלס</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%9E%D7%A9%D7%95%D7%9C%D7%A9%D7%AA" title="התפלגות משולשת">משולשת</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%A4%D7%90%D7%A8%D7%98%D7%95" title="התפלגות פארטו">פארטו</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%A8%D7%99%D7%99%D7%9C%D7%99" title="התפלגות ריילי">ריילי</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%A7%D7%95%D7%A9%D7%99" title="התפלגות קושי">קושי</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%9B%D7%99_%D7%91%D7%A8%D7%99%D7%91%D7%95%D7%A2" title="התפלגות כי בריבוע">כי בריבוע</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%97%D7%A6%D7%99_%D7%94%D7%9E%D7%A2%D7%92%D7%9C_%D7%A9%D7%9C_%D7%95%D7%99%D7%92%D7%A0%D7%A8" title="התפלגות חצי המעגל של ויגנר">חצי המעגל של ויגנר</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%98%D7%A8%D7%99%D7%99%D7%A1%D7%99-%D7%95%D7%99%D7%93%D7%95%D7%9D" title="התפלגות טרייסי-וידום">התפלגות טרייסי-וידום</a> </td></tr> <tr> <td style="background-color: #F2F3F4; text-align: right; font-weight: bold; padding-left: 5px;">התפלגויות ב<a href="/wiki/%D7%A4%D7%99%D7%96%D7%99%D7%A7%D7%94_%D7%A1%D7%98%D7%98%D7%99%D7%A1%D7%98%D7%99%D7%AA" title="פיזיקה סטטיסטית">פיזיקה סטטיסטית</a> </td> <td style="padding-right: 5px; text-align: right;"><a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%91%D7%95%D7%9C%D7%A6%D7%9E%D7%9F" title="התפלגות בולצמן">בולצמן</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%91%D7%95%D7%96-%D7%90%D7%99%D7%99%D7%A0%D7%A9%D7%98%D7%99%D7%99%D7%9F" title="התפלגות בוז-איינשטיין">בוז-איינשטיין</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%9E%D7%A7%D7%A1%D7%95%D7%95%D7%9C-%D7%91%D7%95%D7%9C%D7%A6%D7%9E%D7%9F" title="התפלגות מקסוול-בולצמן">מקסוול-בולצמן</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%A4%D7%A8%D7%9E%D7%99-%D7%93%D7%99%D7%A8%D7%90%D7%A7" title="התפלגות פרמי-דיראק">פרמי-דיראק</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%96%D7%98%D7%90" title="התפלגות זטא">זטא</a> </td></tr> <tr> <td style="background-color: #F2F3F4; text-align: right; font-weight: bold; padding-left: 5px;">התפלגויות נוספות </td> <td style="padding-right: 5px; text-align: right;"><a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_t" title="התפלגות t">התפלגות t</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_F" title="התפלגות F">התפלגות F</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%90%D7%A8%D7%9C%D7%A0%D7%92" title="התפלגות ארלנג">ארלנג</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%95%D7%99%D7%99%D7%91%D7%95%D7%9C" title="התפלגות וייבול">וייבול</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%9C%D7%95%D7%92%D7%99%D7%A1%D7%98%D7%99%D7%AA" title="התפלגות לוגיסטית">לוגיסטית</a> </td></tr> <tr> <td style="background-color: #F2F3F4; text-align: right; font-weight: bold; padding-left: 5px;"><a href="/wiki/%D7%A7%D7%98%D7%92%D7%95%D7%A8%D7%99%D7%94:%D7%A1%D7%95%D7%92%D7%99_%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%99%D7%95%D7%AA" title="קטגוריה:סוגי התפלגויות">סוגי התפלגויות</a> </td> <td style="padding-right: 5px; text-align: right;"><a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%91%D7%93%D7%99%D7%93%D7%94" title="התפלגות בדידה">בדידה</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%A8%D7%A6%D7%99%D7%A4%D7%94" class="mw-redirect" title="התפלגות רציפה">רציפה</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%9E%D7%95%D7%AA%D7%A0%D7%99%D7%AA" title="התפלגות מותנית">מותנית</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%A0%D7%95%D7%A8%D7%9E%D7%9C%D7%99%D7%AA_%D7%9E%D7%95%D7%9B%D7%9C%D7%9C%D7%AA" title="התפלגות נורמלית מוכללת">נורמלית מוכללת</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%96%D7%A0%D7%91_%D7%A2%D7%91%D7%94" title="התפלגות זנב עבה">זנב עבה</a> • <a href="/w/index.php?title=%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%9C%D7%90_%D7%A4%D7%A8%D7%99%D7%A7%D7%94&action=edit&redlink=1" class="new" title="התפלגות לא פריקה (הדף אינו קיים)">לא פריקה</a> • <a href="/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%9E%D7%A9%D7%95%D7%AA%D7%A4%D7%AA" title="התפלגות משותפת">משותפת</a> </td></tr> </tbody></table> <p><br /> </p> <div role="navigation" class="navbox authority-control" aria-labelledby="בקרת_זהויות_15px&#124;link=https&#58;//www.wikidata.org/wiki/Q185547?uselang=he&#124;עריכת_הנתון_בוויקינתונים" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th id="בקרת_זהויות_15px&#124;link=https&#58;//www.wikidata.org/wiki/Q185547?uselang=he&#124;עריכת_הנתון_בוויקינתונים" scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%D7%A2%D7%96%D7%A8%D7%94:%D7%91%D7%A7%D7%A8%D7%AA_%D7%96%D7%94%D7%95%D7%99%D7%95%D7%AA" title="עזרה:בקרת זהויות">בקרת זהויות</a> <span typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q185547?uselang=he" title="עריכת הנתון בוויקינתונים"><img alt="עריכת הנתון בוויקינתונים" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Blue_pencil_RTL.svg/15px-Blue_pencil_RTL.svg.png" decoding="async" width="15" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Blue_pencil_RTL.svg/23px-Blue_pencil_RTL.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Blue_pencil_RTL.svg/30px-Blue_pencil_RTL.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></th><td class="navbox-list navbox-odd" style="text-align:left;border-right-width:2px;border-right-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><div dir="ltr"> <ul><li><span class="nowrap"><a href="/wiki/%D7%94%D7%A1%D7%A4%D7%A8%D7%99%D7%99%D7%94_%D7%94%D7%9C%D7%90%D7%95%D7%9E%D7%99%D7%AA" title="הספרייה הלאומית">NLI</a>: <span class="uid"><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007282570105171">987007282570105171</a></span></span></li> <li><span class="nowrap"><a href="/wiki/%D7%A7%D7%95%D7%91%D7%A5_%D7%91%D7%A7%D7%A8%D7%94_%D7%9E%D7%A9%D7%95%D7%9C%D7%91" title="קובץ בקרה משולב">GND</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4145587-3">4145587-3</a></span></span></li> <li><span class="nowrap"><a href="/wiki/%D7%A9%D7%99%D7%98%D7%AA_%D7%A1%D7%A4%D7%A8%D7%99%D7%99%D7%AA_%D7%94%D7%A7%D7%95%D7%A0%D7%92%D7%A8%D7%A1" title="שיטת ספריית הקונגרס">LCCN</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/subjects/sh85014113">sh85014113</a></span></span></li> <li><span class="nowrap"><a href="/wiki/%D7%94%D7%A1%D7%A4%D7%A8%D7%99%D7%99%D7%94_%D7%94%D7%9C%D7%90%D7%95%D7%9E%D7%99%D7%AA_%D7%A9%D7%9C_%D7%9C%D7%98%D7%91%D7%99%D7%94" title="הספרייה הלאומית של לטביה">LNB</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://kopkatalogs.lv/F?func=direct&local_base=lnc10&doc_number=000327257&P_CON_LNG=ENG">000327257</a></span></span></li> <li><span class="nowrap"><a href="/wiki/%D7%94%D7%A1%D7%A4%D7%A8%D7%99%D7%99%D7%94_%D7%94%D7%9C%D7%90%D7%95%D7%9E%D7%99%D7%AA_%D7%A9%D7%9C_%D7%A6%27%D7%9B%D7%99%D7%94" title="הספרייה הלאומית של צ'כיה">NKC</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph249419&CON_LNG=ENG">ph249419</a></span></span></li></ul> </div></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">אוחזר מתוך "<a dir="ltr" href="https://he.wikipedia.org/w/index.php?title=התפלגות_בינומית&oldid=38186496">https://he.wikipedia.org/w/index.php?title=התפלגות_בינומית&oldid=38186496</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%D7%95%D7%99%D7%A7%D7%99%D7%A4%D7%93%D7%99%D7%94:%D7%A7%D7%98%D7%92%D7%95%D7%A8%D7%99%D7%94" title="ויקיפדיה:קטגוריה">קטגוריה</a>: <ul><li><a href="/wiki/%D7%A7%D7%98%D7%92%D7%95%D7%A8%D7%99%D7%94:%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%99%D7%95%D7%AA_%D7%91%D7%93%D7%99%D7%93%D7%95%D7%AA" title="קטגוריה:התפלגויות בדידות">התפלגויות בדידות</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">קטגוריות מוסתרות: <ul><li><a href="/wiki/%D7%A7%D7%98%D7%92%D7%95%D7%A8%D7%99%D7%94:%D7%A2%D7%A8%D7%9B%D7%99%D7%9D_%D7%A2%D7%9D_%D7%AA%D7%91%D7%A0%D7%99%D7%AA_%D7%91%D7%A8%D7%99%D7%98%D7%A0%D7%99%D7%A7%D7%94" title="קטגוריה:ערכים עם תבנית בריטניקה">ערכים עם תבנית בריטניקה</a></li><li><a href="/wiki/%D7%A7%D7%98%D7%92%D7%95%D7%A8%D7%99%D7%94:%D7%95%D7%99%D7%A7%D7%99%D7%A4%D7%93%D7%99%D7%94:_%D7%A2%D7%A8%D7%9B%D7%99%D7%9D_%D7%A2%D7%9D_%D7%9E%D7%96%D7%94%D7%94_J9U" title="קטגוריה:ויקיפדיה: ערכים עם מזהה J9U">ויקיפדיה: ערכים עם מזהה J9U</a></li><li><a href="/wiki/%D7%A7%D7%98%D7%92%D7%95%D7%A8%D7%99%D7%94:%D7%95%D7%99%D7%A7%D7%99%D7%A4%D7%93%D7%99%D7%94:_%D7%A2%D7%A8%D7%9B%D7%99%D7%9D_%D7%A2%D7%9D_%D7%9E%D7%96%D7%94%D7%94_GND" title="קטגוריה:ויקיפדיה: ערכים עם מזהה GND">ויקיפדיה: ערכים עם מזהה GND</a></li><li><a href="/wiki/%D7%A7%D7%98%D7%92%D7%95%D7%A8%D7%99%D7%94:%D7%95%D7%99%D7%A7%D7%99%D7%A4%D7%93%D7%99%D7%94:_%D7%A2%D7%A8%D7%9B%D7%99%D7%9D_%D7%A2%D7%9D_%D7%9E%D7%96%D7%94%D7%94_LCCN" title="קטגוריה:ויקיפדיה: ערכים עם מזהה LCCN">ויקיפדיה: ערכים עם מזהה LCCN</a></li><li><a href="/wiki/%D7%A7%D7%98%D7%92%D7%95%D7%A8%D7%99%D7%94:%D7%95%D7%99%D7%A7%D7%99%D7%A4%D7%93%D7%99%D7%94:_%D7%A2%D7%A8%D7%9B%D7%99%D7%9D_%D7%A2%D7%9D_%D7%9E%D7%96%D7%94%D7%94_LNB" title="קטגוריה:ויקיפדיה: ערכים עם מזהה LNB">ויקיפדיה: ערכים עם מזהה LNB</a></li><li><a href="/wiki/%D7%A7%D7%98%D7%92%D7%95%D7%A8%D7%99%D7%94:%D7%95%D7%99%D7%A7%D7%99%D7%A4%D7%93%D7%99%D7%94:_%D7%A2%D7%A8%D7%9B%D7%99%D7%9D_%D7%A2%D7%9D_%D7%9E%D7%96%D7%94%D7%94_NKC" 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