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data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Главно мени</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">премести во страничникот</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">скриј</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Прегледник </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/%D0%93%D0%BB%D0%B0%D0%B2%D0%BD%D0%B0_%D1%81%D1%82%D1%80%D0%B0%D0%BD%D0%B8%D1%86%D0%B0" title="Посети главна страница [z]" accesskey="z"><span>Главна страница</span></a></li><li id="n-Што-е-Википедија?" class="mw-list-item"><a href="/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%92%D0%BE%D0%B2%D0%B5%D0%B4"><span>Што е Википедија?</span></a></li><li id="n-featuredcontent" class="mw-list-item"><a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:%D0%98%D0%B7%D0%B1%D1%80%D0%B0%D0%BD%D0%B8_%D1%81%D1%82%D0%B0%D1%82%D0%B8%D0%B8"><span>Избрана содржина</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%A1%D0%BB%D1%83%D1%87%D0%B0%D1%98%D0%BD%D0%B0" title="Вчитај случајна страница [x]" accesskey="x"><span>Случајна страница</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%9F%D0%BE%D1%80%D1%82%D0%B0%D0%BB" title="За проектот, што можете да направите, каде да најдете некои работи"><span>Портал</span></a></li> </ul> </div> </div> <div id="p-interaction" class="vector-menu mw-portlet mw-portlet-interaction" > <div class="vector-menu-heading"> технички </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-Тековни-настани" class="mw-list-item"><a href="/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%A2%D0%B5%D0%BA%D0%BE%D0%B2%D0%BD%D0%B8_%D0%BD%D0%B0%D1%81%D1%82%D0%B0%D0%BD%D0%B8"><span>Тековни настани</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%A1%D0%BA%D0%BE%D1%80%D0%B5%D1%88%D0%BD%D0%B8%D0%9F%D1%80%D0%BE%D0%BC%D0%B5%D0%BD%D0%B8" title="Список на скорешни промени на викито. 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Прочитајте ги правилата и вклучете се!\n\u003C/p\u003E\u003C/div\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="Мрежно место"> <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="Содржина" 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">Содржина</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">премести во страничникот</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">скриј</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">Почеток</div> </a> </li> <li id="toc-Опис_на_нормалната_распределба" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Опис_на_нормалната_распределба"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Опис на нормалната распределба</span> </div> </a> <button aria-controls="toc-Опис_на_нормалната_распределба-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>Префрли на пододделот Опис на нормалната распределба</span> </button> <ul id="toc-Опис_на_нормалната_распределба-sublist" class="vector-toc-list"> <li id="toc-Функција_на_густина_на_веројатност_на_нормална_распределба" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Функција_на_густина_на_веројатност_на_нормална_распределба"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Функција на густина на веројатност на нормална распределба</span> </div> </a> <ul id="toc-Функција_на_густина_на_веројатност_на_нормална_распределба-sublist" class="vector-toc-list"> <li id="toc-Својства_на_нормални_распределби" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Својства_на_нормални_распределби"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.1</span> <span>Својства на нормални распределби</span> </div> </a> <ul id="toc-Својства_на_нормални_распределби-sublist" class="vector-toc-list"> <li id="toc-Кумулативна_функција_на_нормална_распределба" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Кумулативна_функција_на_нормална_распределба"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.1.1</span> <span>Кумулативна функција на нормална распределба</span> </div> </a> <ul id="toc-Кумулативна_функција_на_нормална_распределба-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Стандардна_нормална_распределба" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Стандардна_нормална_распределба"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Стандардна нормална распределба</span> </div> </a> <button aria-controls="toc-Стандардна_нормална_распределба-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>Префрли на пододделот Стандардна нормална распределба</span> </button> <ul id="toc-Стандардна_нормална_распределба-sublist" class="vector-toc-list"> <li id="toc-Параметри_на_стандардната_нормална_распределба:" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Параметри_на_стандардната_нормална_распределба:"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Параметри на стандардната нормална распределба:</span> </div> </a> <ul id="toc-Параметри_на_стандардната_нормална_распределба:-sublist" class="vector-toc-list"> <li id="toc-Кумулативна_функција_на_стандардна_нормална_распределба:" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Кумулативна_функција_на_стандардна_нормална_распределба:"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.1</span> <span>Кумулативна функција на стандардна нормална распределба:</span> </div> </a> <ul id="toc-Кумулативна_функција_на_стандардна_нормална_распределба:-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Наводи" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Наводи"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Наводи</span> </div> </a> <ul id="toc-Наводи-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="Содржина" 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="Прик./скр. содржина" > <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">Прик./скр. содржина</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">Нормална распределба</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="Појдете на статија на друг јазик. Достапно на 73 јазици" > <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-73" 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">73 јазици</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Normalverteilung" title="Normalverteilung — швајцарски германски" lang="gsw" hreflang="gsw" data-title="Normalverteilung" data-language-autonym="Alemannisch" data-language-local-name="швајцарски германски" class="interlanguage-link-target"><span>Alemannisch</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%A7%D8%AD%D8%AA%D9%85%D8%A7%D9%84%D9%8A_%D8%B7%D8%A8%D9%8A%D8%B9%D9%8A" title="توزيع احتمالي طبيعي — арапски" lang="ar" hreflang="ar" data-title="توزيع احتمالي طبيعي" data-language-autonym="العربية" data-language-local-name="арапски" 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_normal" title="Distribución normal — астурски" lang="ast" hreflang="ast" data-title="Distribución normal" data-language-autonym="Asturianu" data-language-local-name="астурски" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Normal_paylanma" title="Normal paylanma — азербејџански" lang="az" hreflang="az" data-title="Normal paylanma" data-language-autonym="Azərbaycanca" data-language-local-name="азербејџански" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D9%86%D9%88%D8%B1%D9%85%D8%A7%D9%84_%D8%AF%D8%A7%D8%BA%DB%8C%D9%84%DB%8C%D9%85" title="نورمال داغیلیم — South Azerbaijani" lang="azb" hreflang="azb" data-title="نورمال داغیلیم" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Si%C3%B4ng-th%C3%A0i_hun-p%C3%B2%CD%98" title="Siông-thài hun-pò͘ — јужномински" lang="nan" hreflang="nan" data-title="Siông-thài hun-pò͘" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="јужномински" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9D%D0%B0%D1%80%D0%BC%D0%B0%D0%BB%D1%8C%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="Нармальнае размеркаванне — белоруски" lang="be" hreflang="be" data-title="Нармальнае размеркаванне" data-language-autonym="Беларуская" data-language-local-name="белоруски" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%D0%BD%D0%BE_%D1%80%D0%B0%D0%B7%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D0%B5%D0%BD%D0%B8%D0%B5" title="Нормално разпределение — бугарски" lang="bg" hreflang="bg" data-title="Нормално разпределение" data-language-autonym="Български" data-language-local-name="бугарски" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Normalna_raspodjela" title="Normalna raspodjela — босански" lang="bs" hreflang="bs" data-title="Normalna raspodjela" data-language-autonym="Bosanski" data-language-local-name="босански" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Distribuci%C3%B3_normal" title="Distribució normal — каталонски" lang="ca" hreflang="ca" data-title="Distribució normal" data-language-autonym="Català" data-language-local-name="каталонски" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%93%D0%B0%D1%83%D1%81%D1%81_%D0%B2%D0%B0%D0%BB%D0%B5%C3%A7%C4%95%D0%B2%C4%95" title="Гаусс валеçĕвĕ — чувашки" lang="cv" hreflang="cv" data-title="Гаусс валеçĕвĕ" data-language-autonym="Чӑвашла" data-language-local-name="чувашки" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Norm%C3%A1ln%C3%AD_rozd%C4%9Blen%C3%AD" title="Normální rozdělení — чешки" lang="cs" hreflang="cs" data-title="Normální rozdělení" data-language-autonym="Čeština" data-language-local-name="чешки" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Dosraniad_normal" title="Dosraniad normal — велшки" lang="cy" hreflang="cy" data-title="Dosraniad normal" data-language-autonym="Cymraeg" data-language-local-name="велшки" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Normalfordeling" title="Normalfordeling — дански" lang="da" hreflang="da" data-title="Normalfordeling" data-language-autonym="Dansk" data-language-local-name="дански" 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/Normalverteilung" title="Normalverteilung — германски" lang="de" hreflang="de" data-title="Normalverteilung" data-language-autonym="Deutsch" data-language-local-name="германски" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Normaaljaotus" title="Normaaljaotus — естонски" lang="et" hreflang="et" data-title="Normaaljaotus" data-language-autonym="Eesti" data-language-local-name="естонски" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9A%CE%B1%CE%BD%CE%BF%CE%BD%CE%B9%CE%BA%CE%AE_%CE%BA%CE%B1%CF%84%CE%B1%CE%BD%CE%BF%CE%BC%CE%AE" title="Κανονική κατανομή — грчки" lang="el" hreflang="el" data-title="Κανονική κατανομή" data-language-autonym="Ελληνικά" data-language-local-name="грчки" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Normal_distribution" title="Normal distribution — англиски" lang="en" hreflang="en" data-title="Normal distribution" data-language-autonym="English" data-language-local-name="англиски" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Distribuci%C3%B3n_normal" title="Distribución normal — шпански" lang="es" hreflang="es" data-title="Distribución normal" data-language-autonym="Español" data-language-local-name="шпански" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Normala_distribuo" title="Normala distribuo — есперанто" lang="eo" hreflang="eo" data-title="Normala distribuo" data-language-autonym="Esperanto" data-language-local-name="есперанто" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Banaketa_normal" title="Banaketa normal — баскиски" lang="eu" hreflang="eu" data-title="Banaketa normal" data-language-autonym="Euskara" data-language-local-name="баскиски" 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_%D9%86%D8%B1%D9%85%D8%A7%D9%84" title="توزیع نرمال — персиски" lang="fa" hreflang="fa" data-title="توزیع نرمال" data-language-autonym="فارسی" data-language-local-name="персиски" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr badge-Q17437798 badge-goodarticle mw-list-item" title="добра статија"><a href="https://fr.wikipedia.org/wiki/Loi_normale" title="Loi normale — француски" lang="fr" hreflang="fr" data-title="Loi normale" data-language-autonym="Français" data-language-local-name="француски" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/D%C3%A1ileadh_normalach" title="Dáileadh normalach — ирски" lang="ga" hreflang="ga" data-title="Dáileadh normalach" data-language-autonym="Gaeilge" data-language-local-name="ирски" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Distribuci%C3%B3n_normal" title="Distribución normal — галициски" lang="gl" hreflang="gl" data-title="Distribución normal" data-language-autonym="Galego" data-language-local-name="галициски" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A0%95%EA%B7%9C_%EB%B6%84%ED%8F%AC" title="정규 분포 — корејски" lang="ko" hreflang="ko" data-title="정규 분포" data-language-autonym="한국어" data-language-local-name="корејски" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%86%D5%B8%D6%80%D5%B4%D5%A1%D5%AC_%D5%A2%D5%A1%D5%B7%D5%AD%D5%B8%D6%82%D5%B4" title="Նորմալ բաշխում — ерменски" lang="hy" hreflang="hy" data-title="Նորմալ բաշխում" data-language-autonym="Հայերեն" data-language-local-name="ерменски" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%B8%E0%A4%BE%E0%A4%AE%E0%A4%BE%E0%A4%A8%E0%A5%8D%E0%A4%AF_%E0%A4%AC%E0%A4%82%E0%A4%9F%E0%A4%A8" title="प्रसामान्य बंटन — хинди" lang="hi" hreflang="hi" data-title="प्रसामान्य बंटन" data-language-autonym="हिन्दी" data-language-local-name="хинди" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Normalna_raspodjela" title="Normalna raspodjela — хрватски" lang="hr" hreflang="hr" data-title="Normalna raspodjela" data-language-autonym="Hrvatski" data-language-local-name="хрватски" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Distribusi_normal" title="Distribusi normal — индонезиски" lang="id" hreflang="id" data-title="Distribusi normal" data-language-autonym="Bahasa Indonesia" data-language-local-name="индонезиски" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Normaldreifing" title="Normaldreifing — исландски" lang="is" hreflang="is" data-title="Normaldreifing" data-language-autonym="Íslenska" data-language-local-name="исландски" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Distribuzione_normale" title="Distribuzione normale — италијански" lang="it" hreflang="it" data-title="Distribuzione normale" data-language-autonym="Italiano" data-language-local-name="италијански" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%A0%D7%95%D7%A8%D7%9E%D7%9C%D7%99%D7%AA" title="התפלגות נורמלית — хебрејски" lang="he" hreflang="he" data-title="התפלגות נורמלית" data-language-autonym="עברית" data-language-local-name="хебрејски" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9C%E1%83%9D%E1%83%A0%E1%83%9B%E1%83%90%E1%83%9A%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%92%E1%83%90%E1%83%9C%E1%83%90%E1%83%AC%E1%83%98%E1%83%9A%E1%83%94%E1%83%91%E1%83%90" title="ნორმალური განაწილება — грузиски" lang="ka" hreflang="ka" data-title="ნორმალური განაწილება" data-language-autonym="ქართული" data-language-local-name="грузиски" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D2%9A%D0%B0%D0%BB%D1%8B%D0%BF%D1%82%D1%8B_%D0%B4%D0%B8%D1%81%D0%BF%D0%B5%D1%80%D1%81%D0%B8%D1%8F" title="Қалыпты дисперсия — казашки" lang="kk" hreflang="kk" data-title="Қалыпты дисперсия" data-language-autonym="Қазақша" data-language-local-name="казашки" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Distributio_normalis" title="Distributio normalis — латински" lang="la" hreflang="la" data-title="Distributio normalis" data-language-autonym="Latina" data-language-local-name="латински" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Norm%C4%81lais_sadal%C4%ABjums" title="Normālais sadalījums — латвиски" lang="lv" hreflang="lv" data-title="Normālais sadalījums" data-language-autonym="Latviešu" data-language-local-name="латвиски" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Normalusis_skirstinys" title="Normalusis skirstinys — литвански" lang="lt" hreflang="lt" data-title="Normalusis skirstinys" data-language-autonym="Lietuvių" data-language-local-name="литвански" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Distribuzzion_normala" title="Distribuzzion normala — ломбардиски" lang="lmo" hreflang="lmo" data-title="Distribuzzion normala" data-language-autonym="Lombard" data-language-local-name="ломбардиски" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Norm%C3%A1lis_eloszl%C3%A1s" title="Normális eloszlás — унгарски" lang="hu" hreflang="hu" data-title="Normális eloszlás" data-language-autonym="Magyar" data-language-local-name="унгарски" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B8%E0%A4%BE%E0%A4%AE%E0%A4%BE%E0%A4%A8%E0%A5%8D%E0%A4%AF_%E0%A4%B5%E0%A4%BF%E0%A4%A4%E0%A4%B0%E0%A4%A3" title="सामान्य वितरण — марати" lang="mr" hreflang="mr" data-title="सामान्य वितरण" data-language-autonym="मराठी" data-language-local-name="марати" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Taburan_normal" title="Taburan normal — малајски" lang="ms" hreflang="ms" data-title="Taburan normal" data-language-autonym="Bahasa Melayu" data-language-local-name="малајски" 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/Normale_verdeling" title="Normale verdeling — холандски" lang="nl" hreflang="nl" data-title="Normale verdeling" data-language-autonym="Nederlands" data-language-local-name="холандски" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%AD%A3%E8%A6%8F%E5%88%86%E5%B8%83" title="正規分布 — јапонски" lang="ja" hreflang="ja" data-title="正規分布" data-language-autonym="日本語" data-language-local-name="јапонски" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Normoolferdialang" title="Normoolferdialang — севернофризиски" lang="frr" hreflang="frr" data-title="Normoolferdialang" data-language-autonym="Nordfriisk" data-language-local-name="севернофризиски" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Normalfordeling" title="Normalfordeling — норвешки букмол" lang="nb" hreflang="nb" data-title="Normalfordeling" data-language-autonym="Norsk bokmål" data-language-local-name="норвешки букмол" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Normalfordeling" title="Normalfordeling — норвешки нинорск" lang="nn" hreflang="nn" data-title="Normalfordeling" data-language-autonym="Norsk nynorsk" data-language-local-name="норвешки нинорск" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Distribussion_%C3%ABd_Gauss" title="Distribussion ëd Gauss — пиемонтски" lang="pms" hreflang="pms" data-title="Distribussion ëd Gauss" data-language-autonym="Piemontèis" data-language-local-name="пиемонтски" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Rozk%C5%82ad_normalny" title="Rozkład normalny — полски" lang="pl" hreflang="pl" data-title="Rozkład normalny" data-language-autonym="Polski" data-language-local-name="полски" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt badge-Q17437796 badge-featuredarticle mw-list-item" title="избрана статија"><a href="https://pt.wikipedia.org/wiki/Distribui%C3%A7%C3%A3o_normal" title="Distribuição normal — португалски" lang="pt" hreflang="pt" data-title="Distribuição normal" data-language-autonym="Português" data-language-local-name="португалски" 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_Gauss" title="Distribuția Gauss — романски" lang="ro" hreflang="ro" data-title="Distribuția Gauss" data-language-autonym="Română" data-language-local-name="романски" 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%9D%D0%BE%D1%80%D0%BC%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="Нормальное распределение — руски" lang="ru" hreflang="ru" data-title="Нормальное распределение" data-language-autonym="Русский" data-language-local-name="руски" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Shp%C3%ABrndarja_normale" title="Shpërndarja normale — албански" lang="sq" hreflang="sq" data-title="Shpërndarja normale" data-language-autonym="Shqip" data-language-local-name="албански" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Normal_distribution" title="Normal distribution — Simple English" lang="en-simple" hreflang="en-simple" data-title="Normal distribution" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Norm%C3%A1lne_rozdelenie" title="Normálne rozdelenie — словачки" lang="sk" hreflang="sk" data-title="Normálne rozdelenie" data-language-autonym="Slovenčina" data-language-local-name="словачки" 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/Normalna_porazdelitev" title="Normalna porazdelitev — словенечки" lang="sl" hreflang="sl" data-title="Normalna porazdelitev" data-language-autonym="Slovenščina" data-language-local-name="словенечки" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%D0%BD%D0%B0_%D1%80%D0%B0%D1%81%D0%BF%D0%BE%D0%B4%D0%B5%D0%BB%D0%B0" title="Нормална расподела — српски" lang="sr" hreflang="sr" data-title="Нормална расподела" data-language-autonym="Српски / srpski" data-language-local-name="српски" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Normalna_raspodela" title="Normalna raspodela — српскохрватски" lang="sh" hreflang="sh" data-title="Normalna raspodela" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="српскохрватски" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Sebaran_normal" title="Sebaran normal — сундски" lang="su" hreflang="su" data-title="Sebaran normal" data-language-autonym="Sunda" data-language-local-name="сундски" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Normaalijakauma" title="Normaalijakauma — фински" lang="fi" hreflang="fi" data-title="Normaalijakauma" data-language-autonym="Suomi" data-language-local-name="фински" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Normalf%C3%B6rdelning" title="Normalfördelning — шведски" lang="sv" hreflang="sv" data-title="Normalfördelning" data-language-autonym="Svenska" data-language-local-name="шведски" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Distribusyong_normal" title="Distribusyong normal — тагалог" lang="tl" hreflang="tl" data-title="Distribusyong normal" data-language-autonym="Tagalog" data-language-local-name="тагалог" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%87%E0%AE%AF%E0%AE%B2%E0%AF%8D%E0%AE%A8%E0%AE%BF%E0%AE%B2%E0%AF%88%E0%AE%AA%E0%AF%8D_%E0%AE%AA%E0%AE%B0%E0%AE%B5%E0%AE%B2%E0%AF%8D" title="இயல்நிலைப் பரவல் — тамилски" lang="ta" hreflang="ta" data-title="இயல்நிலைப் பரவல்" data-language-autonym="தமிழ்" data-language-local-name="тамилски" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%93%D0%B0%D1%83%D1%81%D1%81_%D0%B1%D2%AF%D0%BB%D0%B5%D0%BD%D0%B5%D1%88%D0%B5" title="Гаусс бүленеше — татарски" lang="tt" hreflang="tt" data-title="Гаусс бүленеше" data-language-autonym="Татарча / tatarça" data-language-local-name="татарски" class="interlanguage-link-target"><span>Татарча / tatarça</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%9B%E0%B8%A3%E0%B8%81%E0%B8%95%E0%B8%B4" title="การแจกแจงปรกติ — тајландски" lang="th" hreflang="th" data-title="การแจกแจงปรกติ" data-language-autonym="ไทย" data-language-local-name="тајландски" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Normal_da%C4%9F%C4%B1l%C4%B1m" title="Normal dağılım — турски" lang="tr" hreflang="tr" data-title="Normal dağılım" data-language-autonym="Türkçe" data-language-local-name="турски" 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%9D%D0%BE%D1%80%D0%BC%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="Нормальний розподіл — украински" lang="uk" hreflang="uk" data-title="Нормальний розподіл" data-language-autonym="Українська" data-language-local-name="украински" 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/%D9%86%D8%A7%D8%B1%D9%85%D9%84_%D8%AA%D9%82%D8%B3%DB%8C%D9%85" title="نارمل تقسیم — урду" lang="ur" hreflang="ur" data-title="نارمل تقسیم" data-language-autonym="اردو" data-language-local-name="урду" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Ph%C3%A2n_ph%E1%BB%91i_chu%E1%BA%A9n" title="Phân phối chuẩn — виетнамски" lang="vi" hreflang="vi" data-title="Phân phối chuẩn" data-language-autonym="Tiếng Việt" data-language-local-name="виетнамски" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83" title="正态分布 — ву" lang="wuu" hreflang="wuu" data-title="正态分布" data-language-autonym="吴语" data-language-local-name="ву" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A0%D7%90%D7%A8%D7%9E%D7%90%D7%9C%D7%A2_%D7%A4%D7%90%D7%A8%D7%98%D7%99%D7%99%D7%9C%D7%95%D7%A0%D7%92" title="נארמאלע פארטיילונג — јидиш" lang="yi" hreflang="yi" data-title="נארמאלע פארטיילונג" data-language-autonym="ייִדיש" data-language-local-name="јидиш" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%B8%B8%E6%85%8B%E5%88%86%E4%BD%88" title="常態分佈 — кантонски" lang="yue" hreflang="yue" data-title="常態分佈" data-language-autonym="粵語" data-language-local-name="кантонски" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83" title="正态分布 — кинески" lang="zh" hreflang="zh" data-title="正态分布" data-language-autonym="中文" data-language-local-name="кинески" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q133871#sitelinks-wikipedia" title="Уредување на меѓујазични врски" class="wbc-editpage">Уреди врски</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Именски простори"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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="Преглед на содржинската страница [c]" accesskey="c"><span>Страница</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%D0%A0%D0%B0%D0%B7%D0%B3%D0%BE%D0%B2%D0%BE%D1%80:%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&action=edit&redlink=1" rel="discussion" class="new" title="Разговор за содржинската страница (страницата не постои) [t]" accesskey="t"><span>Разговор</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="Менување на јазичната варијанта" > <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">македонски</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"> <nav aria-label="Посети"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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"><span>Читај</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&veaction=edit" title="Уредете ја страницава [v]" accesskey="v"><span>Уреди</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&action=edit" title="Уредување на изворниот код на страницава [e]" accesskey="e"><span>Уреди извор</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&action=history" title="Претходни верзии на оваа страница. [h]" accesskey="h"><span>Историја</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Алатки за страници"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="алатник" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-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">алатник</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" 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">Алатки</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">премести во страничникот</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">скриј</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Повеќе можности" > <div class="vector-menu-heading"> Дејства </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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"><span>Читај</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&veaction=edit" title="Уредете ја страницава [v]" accesskey="v"><span>Уреди</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&action=edit" title="Уредување на изворниот код на страницава [e]" accesskey="e"><span>Уреди извор</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&action=history"><span>Историја</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Општо </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%A8%D1%82%D0%BE%D0%92%D0%BE%D0%B4%D0%B8%D0%9E%D0%B2%D0%B4%D0%B5/%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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="Список на сите викистраници што водат овде [j]" accesskey="j"><span>Што води овде</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%BE%D0%B2%D1%80%D0%B7%D0%B0%D0%BD%D0%B8%D0%9F%D1%80%D0%BE%D0%BC%D0%B5%D0%BD%D0%B8/%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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" rel="nofollow" title="Скорешни промени на страници со врски на оваа страница [k]" accesskey="k"><span>Поврзани промени</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%A1%D0%BB%D1%83%D0%B6%D0%B1%D0%B5%D0%BD%D0%B8%D0%A1%D1%82%D1%80%D0%B0%D0%BD%D0%B8%D1%86%D0%B8" title="Список на сите службени страници [q]" accesskey="q"><span>Службени страници</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&oldid=5009585" title="Постојана врска до оваа преработка на 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href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%A1%D0%BA%D1%80%D0%B0%D1%82%D1%83%D0%B2%D0%B0%D1%87%D0%9D%D0%B0URL&url=https%3A%2F%2Fmk.wikipedia.org%2Fwiki%2F%25D0%259D%25D0%25BE%25D1%2580%25D0%25BC%25D0%25B0%25D0%25BB%25D0%25BD%25D0%25B0_%25D1%2580%25D0%25B0%25D1%2581%25D0%25BF%25D1%2580%25D0%25B5%25D0%25B4%25D0%25B5%25D0%25BB%25D0%25B1%25D0%25B0"><span>Дај скратена URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:QrCode&url=https%3A%2F%2Fmk.wikipedia.org%2Fwiki%2F%25D0%259D%25D0%25BE%25D1%2580%25D0%25BC%25D0%25B0%25D0%25BB%25D0%25BD%25D0%25B0_%25D1%2580%25D0%25B0%25D1%2581%25D0%25BF%25D1%2580%25D0%25B5%25D0%25B4%25D0%25B5%25D0%25BB%25D0%25B1%25D0%25B0"><span>Преземи QR-код</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"> Печати/извези </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=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9A%D0%BD%D0%B8%D0%B3%D0%B0&bookcmd=book_creator&referer=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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"><span>Создај книга</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:DownloadAsPdf&page=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&action=show-download-screen"><span>Преземи како PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&printable=yes" title="Верзија за 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class="vector-page-tools-landmark" aria-label="Алатки за страници"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Изглед"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Изглед</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">премести во страничникот</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">скриј</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">Од Википедија — слободната енциклопедија</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="mk" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r4723730">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}body.skin-minerva .mw-parser-output .infobox-header,body.skin-minerva .mw-parser-output .infobox-subheader,body.skin-minerva .mw-parser-output .infobox-above,body.skin-minerva .mw-parser-output .infobox-title,body.skin-minerva .mw-parser-output .infobox-image,body.skin-minerva .mw-parser-output .infobox-full-data,body.skin-minerva .mw-parser-output .infobox-below{text-align:center}</style><style data-mw-deduplicate="TemplateStyles:r4817302">.mw-parser-output .ib-prob-dist{border-collapse:collapse;width:20em}.mw-parser-output .ib-prob-dist td,.mw-parser-output .ib-prob-dist th{border:1px solid #a2a9b1}.mw-parser-output .ib-prob-dist .infobox-subheader{text-align:left}.mw-parser-output .ib-prob-dist-image{background:#ddd;font-weight:bold;text-align:center}</style><table class="infobox ib-prob-dist"><caption class="infobox-title">Нормална распределба</caption><tbody><tr><td colspan="4" class="infobox-image"> <div class="ib-prob-dist-image">Веројатносна густина</div><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/%D0%9F%D0%BE%D0%B4%D0%B0%D1%82%D0%BE%D1%82%D0%B5%D0%BA%D0%B0:Normal_Distribution_PDF.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/74/Normal_Distribution_PDF.svg/220px-Normal_Distribution_PDF.svg.png" decoding="async" width="220" height="141" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/74/Normal_Distribution_PDF.svg/330px-Normal_Distribution_PDF.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/74/Normal_Distribution_PDF.svg/440px-Normal_Distribution_PDF.svg.png 2x" data-file-width="720" data-file-height="460" /></a></span><div class="infobox-caption">Црвената крива е <i>стандардна нормална распределба</i></div></td></tr><tr><td colspan="4" class="infobox-image"> <div class="ib-prob-dist-image">Распределбена функција</div><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/%D0%9F%D0%BE%D0%B4%D0%B0%D1%82%D0%BE%D1%82%D0%B5%D0%BA%D0%B0:Normal_Distribution_CDF.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Normal_Distribution_CDF.svg/220px-Normal_Distribution_CDF.svg.png" decoding="async" width="220" height="141" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Normal_Distribution_CDF.svg/330px-Normal_Distribution_CDF.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Normal_Distribution_CDF.svg/440px-Normal_Distribution_CDF.svg.png 2x" data-file-width="720" data-file-height="460" /></a></span></td></tr><tr><th scope="row" class="infobox-label">Запис</th><td colspan="3" class="infobox-data"> <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 {\mathcal {N}}(\mu ,\sigma ^{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">N</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>μ</mi> <mo>,</mo> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {N}}(\mu ,\sigma ^{2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/863304aaa42a945f2f07d79facc3d2eebc845ce7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.062ex; width:8.966ex; height:3.176ex;" alt="{\displaystyle {\mathcal {N}}(\mu ,\sigma ^{2})}"></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D1%87%D0%BA%D0%B8_%D0%BF%D0%B0%D1%80%D0%B0%D0%BC%D0%B5%D1%82%D0%B0%D1%80" title="Статистички параметар">Параметри</a></th><td colspan="3" class="infobox-data"> <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 \mu \in \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu \in \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a9a48f0e84328dc53dec2ad301bb321c00dcf422" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.92ex; height:2.676ex;" alt="{\displaystyle \mu \in \mathbb {R} }"></span> = средина (положба)<br /><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 \sigma ^{2}\in \mathbb {R} _{>0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>∈</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>></mo> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma ^{2}\in \mathbb {R} _{>0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b81059aaa2db87802908711c7527c0e1d65fc06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.236ex; height:3.009ex;" alt="{\displaystyle \sigma ^{2}\in \mathbb {R} _{>0}}"></span> = варијанса квадриран размер)</td></tr><tr><th scope="row" class="infobox-label"><a href="/w/index.php?title=%D0%9D%D0%BE%D1%81%D0%B8%D1%82%D0%B5%D0%BB_%D0%BD%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&action=edit&redlink=1" class="new" title="Носител на функција (страницата не постои)">Носител</a></th><td colspan="3" class="infobox-data"> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\in \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\in \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a9c6d458566aec47a7259762034790c8981aefab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.848ex; height:2.176ex;" alt="{\displaystyle x\in \mathbb {R} }"></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/w/index.php?title=%D0%92%D0%B5%D1%80%D0%BE%D1%98%D0%B0%D1%82%D0%BD%D0%BE%D1%81%D0%BD%D0%B0_%D0%B3%D1%83%D1%81%D1%82%D0%B8%D0%BD%D0%B0&action=edit&redlink=1" class="new" title="Веројатносна густина (страницата не постои)">ФВГ</a></th><td colspan="3" class="infobox-data"> <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}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> <mi>π</mi> </msqrt> </mrow> </mrow> </mfrac> </mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>x</mi> <mo>−</mo> <mi>μ</mi> </mrow> <mi>σ</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a45cef4ca1e2fcd4d367ecff5806d8a2878d3821" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:16.93ex; height:6.676ex;" alt="{\displaystyle {\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}}}"></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/w/index.php?title=%D0%A0%D0%B0%D1%81%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D0%B1%D0%B5%D0%BD%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&action=edit&redlink=1" class="new" title="Распределбена функција (страницата не постои)">РФ</a></th><td colspan="3" class="infobox-data"> <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}}\left[1+\operatorname {erf} \left({\frac {x-\mu }{\sigma {\sqrt {2}}}}\right)\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> <mrow> <mo>[</mo> <mrow> <mn>1</mn> <mo>+</mo> <mi>erf</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>x</mi> <mo>−</mo> <mi>μ</mi> </mrow> <mrow> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{2}}\left[1+\operatorname {erf} \left({\frac {x-\mu }{\sigma {\sqrt {2}}}}\right)\right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/187f33664b79492eedf4406c66d67f9fe5f524ea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:21.328ex; height:6.509ex;" alt="{\displaystyle {\frac {1}{2}}\left[1+\operatorname {erf} \left({\frac {x-\mu }{\sigma {\sqrt {2}}}}\right)\right]}"></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/w/index.php?title=%D0%9E%D0%B1%D1%80%D0%B0%D1%82%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%B5%D0%BD%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&action=edit&redlink=1" class="new" title="Обратна распределбена функција (страницата не постои)">Квантилна</a></th><td colspan="3" class="infobox-data"> <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 \mu +\sigma {\sqrt {2}}\operatorname {erf} ^{-1}(2p-1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> <mo>+</mo> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <msup> <mi>erf</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>p</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu +\sigma {\sqrt {2}}\operatorname {erf} ^{-1}(2p-1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/510cf4025ba141645f21c7f06866867648d5bc21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.19ex; height:3.176ex;" alt="{\displaystyle \mu +\sigma {\sqrt {2}}\operatorname {erf} ^{-1}(2p-1)}"></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/%D0%9E%D1%87%D0%B5%D0%BA%D1%83%D0%B2%D0%B0%D0%BD%D0%B0_%D0%B2%D1%80%D0%B5%D0%B4%D0%BD%D0%BE%D1%81%D1%82" title="Очекувана вредност">Средина</a></th><td colspan="3" class="infobox-data"> <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 \mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }"></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/%D0%9C%D0%B5%D0%B4%D0%B8%D1%98%D0%B0%D0%BD%D0%B0" title="Медијана">Медијана</a></th><td colspan="3" class="infobox-data"> <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 \mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }"></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D1%81" title="Модус">Модус</a></th><td colspan="3" class="infobox-data"> <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 \mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }"></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/%D0%92%D0%B0%D1%80%D0%B8%D1%98%D0%B0%D0%BD%D1%81%D0%B0" title="Варијанса">Варијанса</a></th><td colspan="3" class="infobox-data"> <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 \sigma ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53a5c55e536acf250c1d3e0f754be5692b843ef5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.385ex; height:2.676ex;" alt="{\displaystyle \sigma ^{2}}"></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/%D0%90%D0%BF%D1%81%D0%BE%D0%BB%D1%83%D1%82%D0%BD%D0%BE_%D0%BE%D1%82%D1%81%D1%82%D0%B0%D0%BF%D1%83%D0%B2%D0%B0%D1%9A%D0%B5" title="Апсолутно отстапување">ПАО</a></th><td colspan="3" class="infobox-data"> <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 \sigma {\sqrt {2/\pi }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>π</mi> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma {\sqrt {2/\pi }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3712c4b0b190f29a0c70285b08a63593ef3e1885" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.31ex; height:4.843ex;" alt="{\displaystyle \sigma {\sqrt {2/\pi }}}"></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/%D0%9A%D0%BE%D0%B5%D1%84%D0%B8%D1%86%D0%B8%D0%B5%D0%BD%D1%82_%D0%BD%D0%B0_%D0%B0%D1%81%D0%B8%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0" title="Коефициент на асиметрија">Накосеност</a></th><td colspan="3" class="infobox-data"> <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950" 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 0}"></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/w/index.php?title=%D0%97%D0%B0%D1%88%D0%B8%D0%BB%D0%B5%D0%BD%D0%BE%D1%81%D1%82_(%D1%81%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0)&action=edit&redlink=1" class="new" title="Зашиленост (статистика) (страницата не постои)">Вишок зашиленост</a></th><td colspan="3" class="infobox-data"> <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950" 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 0}"></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/w/index.php?title=%D0%98%D0%BD%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%86%D0%B8%D1%81%D0%BA%D0%B0_%D0%B5%D0%BD%D1%82%D1%80%D0%BE%D0%BF%D0%B8%D1%98%D0%B0&action=edit&redlink=1" class="new" title="Информациска ентропија (страницата не постои)">Ентропија</a></th><td colspan="3" class="infobox-data"> <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}}\log(2\pi \sigma ^{2})+{\frac {1}{2}}}"> <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>log</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>π</mi> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{2}}\log(2\pi \sigma ^{2})+{\frac {1}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/634a430da247dc60f962d8e9082e7fc549ee80f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:16.885ex; height:5.176ex;" alt="{\displaystyle {\frac {1}{2}}\log(2\pi \sigma ^{2})+{\frac {1}{2}}}"></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/w/index.php?title=%D0%9C%D0%BE%D0%BC%D0%B5%D0%BD%D1%82%D0%BE%D1%82%D0%B2%D0%BE%D1%80%D0%BD%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&action=edit&redlink=1" class="new" title="Моментотворна функција (страницата не постои)">МТФ</a></th><td colspan="3" class="infobox-data"> <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 \exp(\mu t+\sigma ^{2}t^{2}/2)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>exp</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>μ</mi> <mi>t</mi> <mo>+</mo> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \exp(\mu t+\sigma ^{2}t^{2}/2)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b73a531ccd6d15d03c0b80f4707641f57bfd521" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.047ex; height:3.176ex;" alt="{\displaystyle \exp(\mu t+\sigma ^{2}t^{2}/2)}"></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/%D0%9A%D0%B0%D1%80%D0%B0%D0%BA%D1%82%D0%B5%D1%80%D0%B8%D1%81%D1%82%D0%B8%D1%87%D0%BD%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" title="Карактеристична функција">КФ</a></th><td colspan="3" class="infobox-data"> <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 \exp(i\mu t-\sigma ^{2}t^{2}/2)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>exp</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>i</mi> <mi>μ</mi> <mi>t</mi> <mo>−</mo> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \exp(i\mu t-\sigma ^{2}t^{2}/2)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8876b3855a069ca3b9464f56ffd8ab9c4b191c50" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.849ex; height:3.176ex;" alt="{\displaystyle \exp(i\mu t-\sigma ^{2}t^{2}/2)}"></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/w/index.php?title=%D0%A4%D0%B8%D1%88%D0%B5%D1%80%D0%BE%D0%B2%D0%B0_%D0%B8%D0%BD%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%86%D0%B8%D1%98%D0%B0&action=edit&redlink=1" class="new" title="Фишерова информација (страницата не постои)">Фишерова информација</a></th><td colspan="3" class="infobox-data"> <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 {\mathcal {I}}(\mu ,\sigma )={\begin{pmatrix}1/\sigma ^{2}&0\\0&2/\sigma ^{2}\end{pmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">I</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>μ</mi> <mo>,</mo> <mi>σ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {I}}(\mu ,\sigma )={\begin{pmatrix}1/\sigma ^{2}&0\\0&2/\sigma ^{2}\end{pmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffca6c1c08385fa2c44455f67e41efb357d3ad8c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; margin-left: -0.069ex; width:26.148ex; height:6.509ex;" alt="{\displaystyle {\mathcal {I}}(\mu ,\sigma )={\begin{pmatrix}1/\sigma ^{2}&0\\0&2/\sigma ^{2}\end{pmatrix}}}"></span> </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 {\mathcal {I}}(\mu ,\sigma ^{2})={\begin{pmatrix}1/\sigma ^{2}&0\\0&1/(2\sigma ^{4})\end{pmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">I</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>μ</mi> <mo>,</mo> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <mn>2</mn> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {I}}(\mu ,\sigma ^{2})={\begin{pmatrix}1/\sigma ^{2}&0\\0&1/(2\sigma ^{4})\end{pmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2047e1545c0f223d425a34cb783fb2928a87dc2e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; margin-left: -0.069ex; width:30.175ex; height:6.509ex;" alt="{\displaystyle {\mathcal {I}}(\mu ,\sigma ^{2})={\begin{pmatrix}1/\sigma ^{2}&0\\0&1/(2\sigma ^{4})\end{pmatrix}}}"></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/w/index.php?title=%D0%9A%D1%83%D0%BB%D0%B1%D0%B0%D0%BA-%D0%9B%D0%B0%D1%98%D0%B1%D0%BB%D0%B5%D1%80%D0%BE%D0%B2%D0%BE_%D1%80%D0%B0%D0%B7%D0%B8%D0%B4%D1%83%D0%B2%D0%B0%D1%9A%D0%B5&action=edit&redlink=1" class="new" title="Кулбак-Лајблерово разидување (страницата не постои)">Кулбак-Лајблерово разидување</a></th><td colspan="3" class="infobox-data"> <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 \over 2}\left\{\left({\frac {\sigma _{0}}{\sigma _{1}}}\right)^{2}+{\frac {(\mu _{1}-\mu _{0})^{2}}{\sigma _{1}^{2}}}-1+\ln {\sigma _{1}^{2} \over \sigma _{0}^{2}}\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> <mrow> <mo>{</mo> <mrow> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msubsup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mfrac> </mrow> <mo>−</mo> <mn>1</mn> <mo>+</mo> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <msubsup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mfrac> </mrow> </mrow> <mo>}</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {1 \over 2}\left\{\left({\frac {\sigma _{0}}{\sigma _{1}}}\right)^{2}+{\frac {(\mu _{1}-\mu _{0})^{2}}{\sigma _{1}^{2}}}-1+\ln {\sigma _{1}^{2} \over \sigma _{0}^{2}}\right\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd1668ab76d345b5cd802c87a9cd3c4f8e735f30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:40.508ex; height:7.509ex;" alt="{\displaystyle {1 \over 2}\left\{\left({\frac {\sigma _{0}}{\sigma _{1}}}\right)^{2}+{\frac {(\mu _{1}-\mu _{0})^{2}}{\sigma _{1}^{2}}}-1+\ln {\sigma _{1}^{2} \over \sigma _{0}^{2}}\right\}}"></span></td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/%D0%9F%D0%BE%D0%B4%D0%B0%D1%82%D0%BE%D1%82%D0%B5%D0%BA%D0%B0:Normal-tables-in-reverse.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/mk/thumb/d/d9/Normal-tables-in-reverse.jpg/220px-Normal-tables-in-reverse.jpg" decoding="async" width="220" height="125" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/mk/thumb/d/d9/Normal-tables-in-reverse.jpg/330px-Normal-tables-in-reverse.jpg 1.5x, //upload.wikimedia.org/wikipedia/mk/thumb/d/d9/Normal-tables-in-reverse.jpg/440px-Normal-tables-in-reverse.jpg 2x" data-file-width="1024" data-file-height="582" /></a><figcaption>Вкупната плоштина под кривата изнесува 1. X е нормална случајна променлива со кумулативна функција на распределба F (X), а a и b се две можни вредности на X, при што а < b.</figcaption></figure> <p><b>Нормална распределба</b> или <b>Гаусова распределба</b> — <a href="/wiki/%D0%92%D0%B5%D1%80%D0%BE%D1%98%D0%B0%D1%82%D0%BD%D0%BE%D1%81%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="Веројатносна распределба">веројатносна распределба</a> на случајна големина со препознатлива форма во облик на звоно. Нормалната распределба ја открил германскиот <a href="/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика">математичар</a> <a href="/wiki/%D0%9A%D0%B0%D1%80%D0%BB_%D0%A4%D1%80%D0%B8%D0%B4%D1%80%D0%B8%D1%85_%D0%93%D0%B0%D1%83%D1%81" title="Карл Фридрих Гаус">Карл Ф. Гаус</a>, а називот „нормална распределба“ го дал Галтон. Во <a href="/wiki/%D0%95%D0%B2%D1%80%D0%BE%D0%BF%D0%B0" title="Европа">Европа</a>, тој е познат како Гаусова распределба, додека во англосаксонските земји е познат како нормална распределба.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Опис_на_нормалната_распределба"><span id=".D0.9E.D0.BF.D0.B8.D1.81_.D0.BD.D0.B0_.D0.BD.D0.BE.D1.80.D0.BC.D0.B0.D0.BB.D0.BD.D0.B0.D1.82.D0.B0_.D1.80.D0.B0.D1.81.D0.BF.D1.80.D0.B5.D0.B4.D0.B5.D0.BB.D0.B1.D0.B0"></span>Опис на нормалната распределба</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&veaction=edit&section=1" title="Уреди го одделот „Опис на нормалната распределба“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&action=edit&section=1" title="Уреди изворен код на одделот: Опис на нормалната распределба"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Нормалната распределба блиску го апроксимира веројатносната распределба со широк <a href="/w/index.php?title=%D0%98%D0%BD%D1%82%D0%B5%D1%80%D0%B2%D0%B0%D0%BB&action=edit&redlink=1" class="new" title="Интервал (страницата не постои)">интервал</a> на <a href="/wiki/%D0%A1%D0%BB%D1%83%D1%87%D0%B0%D1%98%D0%BD%D0%B8_%D0%BF%D1%80%D0%BE%D0%BC%D0%B5%D0%BD%D0%BB%D0%B8%D0%B2%D0%B8" class="mw-redirect" title="Случајни променливи">случајни променливи</a>. Има бројни <a href="/w/index.php?title=%D0%9F%D1%80%D0%B8%D0%BC%D0%B5%D1%80%D0%B8&action=edit&redlink=1" class="new" title="Примери (страницата не постои)">примери</a> за нормална распределба: вкупните продажби на <a href="/wiki/%D0%9F%D1%80%D0%BE%D0%B8%D0%B7%D0%B2%D0%BE%D0%B4%D1%81%D1%82%D0%B2%D0%BE" title="Производство">производство</a>, моделите на цените на акциите и слично. Нормалната <a href="/wiki/%D0%A1%D0%BB%D1%83%D1%87%D0%B0%D1%98%D0%BD%D0%B0_%D0%BF%D1%80%D0%BE%D0%BC%D0%B5%D0%BD%D0%BB%D0%B8%D0%B2%D0%B0" title="Случајна променлива">случајна променлива</a> X претставува непрекината <a href="/wiki/%D0%9F%D1%80%D0%BE%D0%BC%D0%B5%D0%BD%D0%BB%D0%B8%D0%B2%D0%B0" title="Променлива">променлива</a> која зема бесконечен број на можни вредности од <b>-∞ до +∞</b>, со функција која го претставува распределбата на веројатноста во дадениот <a href="/w/index.php?title=%D0%98%D0%BD%D1%82%D0%B5%D1%80%D0%B2%D0%B0%D0%BB&action=edit&redlink=1" class="new" title="Интервал (страницата не постои)">интервал</a>. Распределбата на средините на примероците се приближуваат кон нормална распределба, ако се работи за големина на <a href="/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D1%87%D0%BA%D0%B8_%D0%BF%D1%80%D0%B8%D0%BC%D0%B5%D1%80%D0%BE%D0%BA" class="mw-redirect" title="Статистички примерок">примерок</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Функција_на_густина_на_веројатност_на_нормална_распределба"><span id=".D0.A4.D1.83.D0.BD.D0.BA.D1.86.D0.B8.D1.98.D0.B0_.D0.BD.D0.B0_.D0.B3.D1.83.D1.81.D1.82.D0.B8.D0.BD.D0.B0_.D0.BD.D0.B0_.D0.B2.D0.B5.D1.80.D0.BE.D1.98.D0.B0.D1.82.D0.BD.D0.BE.D1.81.D1.82_.D0.BD.D0.B0_.D0.BD.D0.BE.D1.80.D0.BC.D0.B0.D0.BB.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"></span>Функција на густина на веројатност на нормална распределба</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&veaction=edit&section=2" title="Уреди го одделот „Функција на густина на веројатност на нормална распределба“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&action=edit&section=2" title="Уреди изворен код на одделот: Функција на густина на веројатност на нормална распределба"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Нормалната распределба на веројатноста претставува големо <a href="/wiki/%D0%9C%D0%BD%D0%BE%D0%B6%D0%B5%D1%81%D1%82%D0%B2%D0%BE" title="Множество">множество</a> на распределби, секој со единствена <a href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%84%D0%B8%D0%BA%D0%B0%D1%86%D0%B8%D1%98%D0%B0&action=edit&redlink=1" class="new" title="Спецификација (страницата не постои)">спецификација</a> за параметрите µ и σ.<sup>2</sup> <sup id="cite_ref-Philippe_Jorion_1997_2-0" class="reference"><a href="#cite_note-Philippe_Jorion_1997-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)={\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}},\,\quad x\in \mathbb {R} ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> <mi>π</mi> </msqrt> </mrow> </mrow> </mfrac> </mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>x</mi> <mo>−</mo> <mi>μ</mi> </mrow> <mi>σ</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </msup> <mo>,</mo> <mspace width="thinmathspace" /> <mspace width="1em" /> <mi>x</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)={\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}},\,\quad x\in \mathbb {R} ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa493c0421b9e851e8b15e4ff05460655cbb6b5d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:34.685ex; height:6.676ex;" alt="{\displaystyle f(x)={\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}},\,\quad x\in \mathbb {R} ,}"></span></dd></dl> <div class="mw-heading mw-heading4"><h4 id="Својства_на_нормални_распределби"><span id=".D0.A1.D0.B2.D0.BE.D1.98.D1.81.D1.82.D0.B2.D0.B0_.D0.BD.D0.B0_.D0.BD.D0.BE.D1.80.D0.BC.D0.B0.D0.BB.D0.BD.D0.B8_.D1.80.D0.B0.D1.81.D0.BF.D1.80.D0.B5.D0.B4.D0.B5.D0.BB.D0.B1.D0.B8"></span>Својства на нормални распределби</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&veaction=edit&section=3" title="Уреди го одделот „Својства на нормални распределби“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&action=edit&section=3" title="Уреди изворен код на одделот: Својства на нормални распределби"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>• <a href="/w/index.php?title=%D0%A1%D1%80%D0%B5%D0%B4%D0%B8%D0%BD%D0%B0&action=edit&redlink=1" class="new" title="Средина (страницата не постои)">Средина</a> на <a href="/w/index.php?title=%D0%A1%D0%BB%D1%83%D1%87%D0%B0%D1%98%D0%BD%D0%B0%D1%82%D0%B0_%D0%BF%D1%80%D0%BE%D0%BC%D0%B5%D0%BD%D0%BB%D0%B8%D0%B2%D0%B0&action=edit&redlink=1" class="new" title="Случајната променлива (страницата не постои)">случајната променлива</a> е µ </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {E} [X]=\mu .\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">E</mi> <mo>⁡</mo> <mo stretchy="false">[</mo> <mi>X</mi> <mo stretchy="false">]</mo> <mo>=</mo> <mi>μ</mi> <mo>.</mo> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {E} [X]=\mu .\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a850f6d56e315eaef8b630976d5164b368ecb072" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:10.391ex; height:2.843ex;" alt="{\displaystyle \operatorname {E} [X]=\mu .\,\!}"></span></dd></dl> <p>• Варијансата на случајната променлива е σ<sup>2</sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {\sigma ^{2}} =\sum _{i=1}^{n}(p_{i}\cdot (x_{i}-\mu )^{2})=\sum _{i=1}^{n}(p_{i}\cdot x_{i}^{2})-\mu ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <mo stretchy="false">(</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>⋅</mo> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>−</mo> <mi>μ</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <mo stretchy="false">(</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>⋅</mo> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo stretchy="false">)</mo> <mo>−</mo> <msup> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {\sigma ^{2}} =\sum _{i=1}^{n}(p_{i}\cdot (x_{i}-\mu )^{2})=\sum _{i=1}^{n}(p_{i}\cdot x_{i}^{2})-\mu ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b107f59526fcd278b80b31172a77b772a036721" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:43.122ex; height:6.843ex;" alt="{\displaystyle \operatorname {\sigma ^{2}} =\sum _{i=1}^{n}(p_{i}\cdot (x_{i}-\mu )^{2})=\sum _{i=1}^{n}(p_{i}\cdot x_{i}^{2})-\mu ^{2}}"></span></dd></dl> <p>• Доколку ја знаеме средината и варијансата, можеме да ја дефинираме нормалната распределба со користење на ознаката </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X\ \sim \ {\mathcal {N}}(\mu ,\,\sigma ^{2}).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> <mtext> </mtext> <mo>∼</mo> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">N</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>μ</mi> <mo>,</mo> <mspace width="thinmathspace" /> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X\ \sim \ {\mathcal {N}}(\mu ,\,\sigma ^{2}).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd6d3a2a9a725c0bb7c43a9139922e903a2a5b34" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.178ex; height:3.176ex;" alt="{\displaystyle X\ \sim \ {\mathcal {N}}(\mu ,\,\sigma ^{2}).}"></span></dd></dl> <p>• <a href="/wiki/%D0%9A%D0%BE%D0%B5%D1%84%D0%B8%D1%86%D0%B8%D0%B5%D0%BD%D1%82%D0%BE%D1%82_%D0%BD%D0%B0_%D0%B0%D1%81%D0%B8%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0" class="mw-redirect" title="Коефициентот на асиметрија">Коефициентот на асиметрија</a> (накосеност) <b>α3=0</b>, а <a href="/w/index.php?title=%D0%97%D0%B0%D1%88%D0%B8%D0%BB%D0%B5%D0%BD%D0%BE%D1%81%D1%82_(%D1%81%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0)&action=edit&redlink=1" class="new" title="Зашиленост (статистика) (страницата не постои)">коефициентот на зашиленост</a> <b>α4=3</b> • Функцијата на густина на веројатноста е унимодална <b>(М=Ме=Мо)</b> Нормалната распределба е <a href="/wiki/%D0%A1%D0%B8%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%87%D0%B5%D0%BD" class="mw-redirect" title="Симетричен">симетричен</a>. Различните <a href="/w/index.php?title=%D0%A6%D0%B5%D0%BD%D1%82%D1%80%D0%B0%D0%BB%D0%BD%D0%B8_%D1%82%D0%B5%D0%BD%D0%B4%D0%B5%D0%BD%D1%86%D0%B8%D0%B8&action=edit&redlink=1" class="new" title="Централни тенденции (страницата не постои)">централни тенденции</a> се прикажуваат со разликите во µ. Разликите во σ<sup>2</sup> резултираат со <a href="/w/index.php?title=%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D0%B8&action=edit&redlink=1" class="new" title="Функции (страницата не постои)">функции</a> на густина со различни <a href="/w/index.php?title=%D0%A8%D0%B8%D1%80%D0%B8%D0%BD%D0%B8&action=edit&redlink=1" class="new" title="Ширини (страницата не постои)">ширини</a>. Средината на распределбата дава мерка на централна <a href="/w/index.php?title=%D0%9B%D0%BE%D0%BA%D0%B0%D1%86%D0%B8%D1%98%D0%B0&action=edit&redlink=1" class="new" title="Локација (страницата не постои)">локација</a>, а варијансата дава мерка на дисперзијата околу средината.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Важна одлика на нормалната распределба е тоа што е целосно определена од нејзините први два моменти: <a href="/w/index.php?title=%D0%A1%D1%80%D0%B5%D0%B4%D0%BD%D0%B0_%D0%B2%D1%80%D0%B5%D0%B4%D0%BD%D0%BE%D1%81%D1%82&action=edit&redlink=1" class="new" title="Средна вредност (страницата не постои)">средната вредност</a> и <a href="/wiki/%D0%92%D0%B0%D1%80%D0%B8%D1%98%D0%B0%D0%BD%D1%81%D0%B0" title="Варијанса">варијансата</a>.<sup id="cite_ref-Philippe_Jorion_1997_2-1" class="reference"><a href="#cite_note-Philippe_Jorion_1997-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading5"><h5 id="Кумулативна_функција_на_нормална_распределба"><span id=".D0.9A.D1.83.D0.BC.D1.83.D0.BB.D0.B0.D1.82.D0.B8.D0.B2.D0.BD.D0.B0_.D1.84.D1.83.D0.BD.D0.BA.D1.86.D0.B8.D1.98.D0.B0_.D0.BD.D0.B0_.D0.BD.D0.BE.D1.80.D0.BC.D0.B0.D0.BB.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"></span>Кумулативна функција на нормална распределба</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&veaction=edit&section=4" title="Уреди го одделот „Кумулативна функција на нормална распределба“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&action=edit&section=4" title="Уреди изворен код на одделот: Кумулативна функција на нормална распределба"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{(}X)=\operatorname {P} (X\leq x),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> </msub> <mi>X</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi mathvariant="normal">P</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>X</mi> <mo>≤</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{(}X)=\operatorname {P} (X\leq x),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0f98e439345e77d9abe8fdeda670279c5ba0054" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:18.797ex; height:3.176ex;" alt="{\displaystyle F_{(}X)=\operatorname {P} (X\leq x),}"></span></dd></dl> <p>Тоа е плоштината под нормалната функција на густината на веројатноста на лево од x. Вкупната <a href="/wiki/%D0%9F%D0%BB%D0%BE%D1%88%D1%82%D0%B8%D0%BD%D0%B0" title="Плоштина">плоштина</a> под кривата изнесува 1. X е <a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%D0%BD%D0%B0&action=edit&redlink=1" class="new" title="Нормална (страницата не постои)">нормална</a> случајна променлива со <a href="/w/index.php?title=%D0%9A%D1%83%D0%BC%D1%83%D0%BB%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&action=edit&redlink=1" class="new" title="Кумулативна функција (страницата не постои)">кумулативна функција</a> на распределба F (X), а a и b се две можни вредности на X, при што а < b. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {P} (a<X\leq b)=F_{X}(b)-F_{X}(a).\int _{a}^{b}f(x)\,dx}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">P</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo><</mo> <mi>X</mi> <mo>≤</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>−</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>.</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {P} (a<X\leq b)=F_{X}(b)-F_{X}(a).\int _{a}^{b}f(x)\,dx}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a18336967d06e9405bf5a663403b3696d5e0bf5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:44.008ex; height:6.343ex;" alt="{\displaystyle \operatorname {P} (a<X\leq b)=F_{X}(b)-F_{X}(a).\int _{a}^{b}f(x)\,dx}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Стандардна_нормална_распределба"><span id=".D0.A1.D1.82.D0.B0.D0.BD.D0.B4.D0.B0.D1.80.D0.B4.D0.BD.D0.B0_.D0.BD.D0.BE.D1.80.D0.BC.D0.B0.D0.BB.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"></span>Стандардна нормална распределба</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&veaction=edit&section=5" title="Уреди го одделот „Стандардна нормална распределба“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&action=edit&section=5" title="Уреди изворен код на одделот: Стандардна нормална распределба"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/%D0%9F%D0%BE%D0%B4%D0%B0%D1%82%D0%BE%D1%82%D0%B5%D0%BA%D0%B0:Standard-normal-distribution.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/mk/thumb/1/1b/Standard-normal-distribution.gif/220px-Standard-normal-distribution.gif" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/mk/thumb/1/1b/Standard-normal-distribution.gif/330px-Standard-normal-distribution.gif 1.5x, //upload.wikimedia.org/wikipedia/mk/1/1b/Standard-normal-distribution.gif 2x" data-file-width="400" data-file-height="300" /></a><figcaption>Стандардна нормална распределба</figcaption></figure> <p>За да може да се врши споредба на распределбите, потребно е нормалната распределба да има единечен <a href="/wiki/%D0%9E%D0%B1%D0%BB%D0%B8%D0%BA" title="Облик">облик</a>, односно облик кој не зависи од параметрите µ и σ<sup>2</sup>. Нормалната распределба која се одликува со средна вредност еднаква на нула и варијанса еднаква на еден (µ=0, σ<sup>2</sup> =1) се нарекува стандардна нормална распределба. Оваа распределба е совршено симетрична, а нејзината средна вредност е еднаква на <a href="/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D1%81" title="Модус">модусот</a> и на <a href="/wiki/%D0%9C%D0%B5%D0%B4%D0%B8%D1%98%D0%B0%D0%BD%D0%B0" title="Медијана">медијаната</a> (чија веројатност за случување изнесува 50%). Притоа, 95% од нормалната распределба ги опфаќа вредностите од две стандардни отстапувања над и под средната вредност, 66% од вредностите се наоѓаат во интервалот од едно стандардно отстапвуање под и над средната вредност, а 99% од вредностите се наоѓаат во интервалот од три стандардни отстапувања над и под средната вредност.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p><i><b>Z ~</b></i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N(0,1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N(0,1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/763663a6c2dbaa4cf12b99c5710e01ff2504f193" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.232ex; height:2.843ex;" alt="{\displaystyle N(0,1)}"></span> </p><p>Можеме да ја добиеме веројатноста за која било нормално распределена <a href="/wiki/%D0%A1%D0%BB%D1%83%D1%87%D0%B0%D1%98%D0%BD%D0%B0_%D0%BF%D1%80%D0%BE%D0%BC%D0%B5%D0%BD%D0%BB%D0%B8%D0%B2%D0%B0" title="Случајна променлива">случајна променлива</a> со тоа што ќе ја претвориме во случајна променлива со стандардна нормална распределба Z. Секогаш постои директна <a href="/w/index.php?title=%D0%97%D0%B0%D0%B2%D0%B8%D1%81%D0%BD%D0%BE%D1%81%D1%82&action=edit&redlink=1" class="new" title="Зависност (страницата не постои)">зависност</a> меѓу било која нормално распределена променлива и Z, а тоа се постигнува со трансформацијата: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z={\frac {X-\mu }{\sigma }},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>X</mi> <mo>−</mo> <mi>μ</mi> </mrow> <mi>σ</mi> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z={\frac {X-\mu }{\sigma }},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a333cf878d9b62884a5113d828d602655e25864" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.484ex; height:5.343ex;" alt="{\displaystyle Z={\frac {X-\mu }{\sigma }},}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Параметри_на_стандардната_нормална_распределба:"><span id=".D0.9F.D0.B0.D1.80.D0.B0.D0.BC.D0.B5.D1.82.D1.80.D0.B8_.D0.BD.D0.B0_.D1.81.D1.82.D0.B0.D0.BD.D0.B4.D0.B0.D1.80.D0.B4.D0.BD.D0.B0.D1.82.D0.B0_.D0.BD.D0.BE.D1.80.D0.BC.D0.B0.D0.BB.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:"></span>Параметри на стандардната нормална распределба:</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&veaction=edit&section=6" title="Уреди го одделот „Параметри на стандардната нормална распределба:“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&action=edit&section=6" title="Уреди изворен код на одделот: Параметри на стандардната нормална распределба:"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Стандардната нормална распределба се одликува со следниве параметри:<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> • Аритметичката средина <i><b> µ = 0 </b></i> • Варијанса <b>σ<sup>2</sup> = 1</b> • Коефициент на асиметрија <b>α3=0</b>, што значи дека распределбата е едномодална и идеално симетрична. • Коефициентот на зашиленост <b>α4=3</b>, што значи дека распределбата има нормална висина. </p> <div class="mw-heading mw-heading4"><h4 id="Кумулативна_функција_на_стандардна_нормална_распределба:"><span id=".D0.9A.D1.83.D0.BC.D1.83.D0.BB.D0.B0.D1.82.D0.B8.D0.B2.D0.BD.D0.B0_.D1.84.D1.83.D0.BD.D0.BA.D1.86.D0.B8.D1.98.D0.B0_.D0.BD.D0.B0_.D1.81.D1.82.D0.B0.D0.BD.D0.B4.D0.B0.D1.80.D0.B4.D0.BD.D0.B0_.D0.BD.D0.BE.D1.80.D0.BC.D0.B0.D0.BB.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:"></span>Кумулативна функција на стандардна нормална распределба:</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&veaction=edit&section=7" title="Уреди го одделот „Кумулативна функција на стандардна нормална распределба:“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&action=edit&section=7" title="Уреди изворен код на одделот: Кумулативна функција на стандардна нормална распределба:"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <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 F_{(}Z)=\operatorname {P} (Z\leq z),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> </msub> <mi>Z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi mathvariant="normal">P</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>Z</mi> <mo>≤</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{(}Z)=\operatorname {P} (Z\leq z),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6f311ee0f6194e765318195df738e06e204ed22" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:17.956ex; height:3.176ex;" alt="{\displaystyle F_{(}Z)=\operatorname {P} (Z\leq z),}"></span> </p><p>Вредностите на кумулативната функција на распределба за <a href="/w/index.php?title=%D0%9D%D0%B5%D0%B3%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%B8_%D0%B2%D1%80%D0%B5%D0%B4%D0%BD%D0%BE%D1%81%D1%82%D0%B8&action=edit&redlink=1" class="new" title="Негативни вредности (страницата не постои)">негативни вредности</a> на Z можат да се утврдат со користење на <a href="/wiki/%D0%A1%D0%B8%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0" title="Симетрија">симетрија</a> на функцијата на густината на веројатноста. </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}(-z<Z\leq z)=2F(z)-1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> <mo stretchy="false">(</mo> <mo>−</mo> <mi>z</mi> <mo><</mo> <mi>Z</mi> <mo>≤</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>2</mn> <mi>F</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {P}(-z<Z\leq z)=2F(z)-1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/002f3029479113fdf48c010ff2ba0b0416bb28c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:28.318ex; height:2.843ex;" alt="{\displaystyle {P}(-z<Z\leq z)=2F(z)-1}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Наводи"><span id=".D0.9D.D0.B0.D0.B2.D0.BE.D0.B4.D0.B8"></span>Наводи</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&veaction=edit&section=8" title="Уреди го одделот „Наводи“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D0%BB%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&action=edit&section=8" title="Уреди изворен код на одделот: Наводи"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">Philippe Jorion (1997): <i>Value at Risk: The New Benchmark for Controlling Market Risk</i>. New York et al.: McGraw-Hill, стр. 72-73.</span> </li> <li id="cite_note-Philippe_Jorion_1997-2"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-Philippe_Jorion_1997_2-0">2,0</a></sup> <sup><a href="#cite_ref-Philippe_Jorion_1997_2-1">2,1</a></sup></span> <span class="reference-text">Philippe Jorion (1997): <i>Value at Risk: The New Benchmark for Controlling Market Risk</i>. New York et al.: McGraw-Hill, стр. 73.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text">Paul Newbold, William Carlson, Betty Tharne (2007): <i>Statistics for business and economics</i>, 6th edition, Pearson.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text">Philippe Jorion (1997): <i>Value at Risk: The New Benchmark for Controlling Market Risk</i>. New York et al.: McGraw-Hill, стр. 73-75.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text">Ристески Славе, Тевдовски, Драган (2010): <i>Статистика за бизнис и економија</i>, четврто издание, Скопје: Економски факултет - Скопје.</span> </li> </ol></div></div></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Преземено од „<a dir="ltr" href="https://mk.wikipedia.org/w/index.php?title=Нормална_распределба&oldid=5009585">https://mk.wikipedia.org/w/index.php?title=Нормална_распределба&oldid=5009585</a>“</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D0%B8" title="Специјална:Категории">Категории</a>: <ul><li><a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:%D0%92%D0%B5%D1%80%D0%BE%D1%98%D0%B0%D1%82%D0%BD%D0%BE%D1%81%D1%82" title="Категорија:Веројатност">Веројатност</a></li><li><a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Категорија:Статистика">Статистика</a></li><li><a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:%D0%92%D0%B5%D1%80%D0%BE%D1%98%D0%B0%D1%82%D0%BD%D0%BE%D1%81%D0%BD%D0%B8_%D1%80%D0%B0%D1%81%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D0%B1%D0%B8" title="Категорија:Веројатносни распределби">Веројатносни распределби</a></li><li><a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:%D0%9D%D0%B5%D0%BF%D1%80%D0%B5%D0%BA%D0%B8%D0%BD%D0%B0%D1%82%D0%B8_%D1%80%D0%B0%D1%81%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D0%B1%D0%B8" title="Категорија:Непрекинати распределби">Непрекинати распределби</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Последната промена на страницава е извршена на 16 јули 2023 г. во 05:26 ч.</li> <li id="footer-info-copyright">Текстот е достапен под условите на лиценцата <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/">Криејтив комонс Наведи извор-Сподели под исти услови</a>. 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