{"id":852,"date":"2026-10-03T17:26:50","date_gmt":"2026-10-03T16:26:50","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/binom-dagilimi-hesaplama\/"},"modified":"2026-10-03T17:26:50","modified_gmt":"2026-10-03T16:26:50","slug":"binom-dagilimi-hesaplama","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/istatistik\/binom-dagilimi-hesaplama\/","title":{"rendered":"Binom Da\u011f\u0131l\u0131m\u0131 Hesaplama Arac\u0131"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Binom Olas\u0131l\u0131klar\u0131n\u0131 Hesaplay\u0131n<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"852\" data-favorite-title=\"Binom Da\u011f\u0131l\u0131m\u0131\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/istatistik\/binom-dagilimi-hesaplama\/\" data-favorite-excerpt=\"Binom olas\u0131l\u0131klar\u0131n\u0131 hesaplay\u0131n: P(X = k), k\u00fcm\u00fclatif P(X \u2264 k), P(X \u2265 k) veya bir ba\u015far\u0131 aral\u0131\u011f\u0131. Deneme say\u0131s\u0131n\u0131, ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131n\u0131 ve k de\u011ferini girerek ortalama, varyans ve standart sapmay\u0131 da elde edin.\" aria-label=\"Favorilere ekle\" data-favorite-icon=\"icon icon-wpcalc-distribution-histogram\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/tr\/istatistik\/binom-dagilimi-hesaplama\/\" method=\"POST\" class=\"calculator\" id=\"calculator-852\" data-post=\"852\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Giri\u015f alanlar\u0131<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Deneme say\u0131s\u0131 (n)<\/label><div class=\"term\">n<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"deneme_says_n\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 10\" min=\"1\" max=\"10000\" value=\"10\"\/><small id=\"calc-info-1\">Ba\u011f\u0131ms\u0131z Bernoulli denemesi say\u0131s\u0131. 1 ile 10.000 aras\u0131nda bir tam say\u0131.<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 (p)<\/label><div class=\"term\">p<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"baar_olasl_p\" id=\"field-2\" aria-describedby=\"calc-unit-2 calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 50\" min=\"0\" max=\"100\" value=\"50\"\/><div class=\"unit\" id=\"calc-unit-2\">%<\/div><small id=\"calc-info-2\">Tek bir denemedeki ba\u015far\u0131 \u015fans\u0131, %0 ile %100 aras\u0131nda.<\/small><\/div><div class=\"field\" id=\"input-3\"><label for=\"field-3\">\u0130lgilenilen ba\u015far\u0131 say\u0131s\u0131<\/label><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"lgilenilen_baar_says\"><option value=\"exact\" selected>Tam olarak k ba\u015far\u0131<\/option><option value=\"range\">k\u2081 ile k\u2082 aras\u0131nda ba\u015far\u0131<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">Ba\u015far\u0131 say\u0131s\u0131 (k)<\/label><div class=\"term\">k<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"baar_says_k\" id=\"field-4\" aria-describedby=\"calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 5\" min=\"0\" value=\"5\"\/><small id=\"calc-info-4\">0 ile n aras\u0131nda bir tam say\u0131. Aral\u0131k modunda bu, alt s\u0131n\u0131r k\u2081&#039;dir.<\/small><\/div><div class=\"field has-term\" id=\"input-5\" hidden><label for=\"field-5\">\u00dcst s\u0131n\u0131r (k\u2082)<\/label><div class=\"term\">k\u2082<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"st_snr_k\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 7\" min=\"0\" value=\"7\"\/><small id=\"calc-info-5\">Aral\u0131\u011f\u0131n \u00fcst s\u0131n\u0131r\u0131. En az k\u2081 olmal\u0131d\u0131r.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"852\">Hesapla<\/button><button type=\"reset\">S\u0131f\u0131rla<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Otomatik hesapla<\/label><small>Etkinle\u015ftirilirse, herhangi bir de\u011feri de\u011fi\u015ftirdi\u011finizde sonu\u00e7 otomatik olarak g\u00fcncellenir.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Sonu\u00e7lar\u0131n\u0131z<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>P(X = k)<\/span><span class=\"result-term\">pmf<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>P(X \u2264 k)<\/span><span class=\"result-term\">cdf<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>P(X \u2265 k)<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-4\"><span class=\"field-title\"><span>P(k\u2081 \u2264 X \u2264 k\u2082)<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-5\"><span class=\"field-title\"><span>Ortalama<\/span><span class=\"result-term\">\u03bc<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-6\"><span class=\"field-title\"><span>Varyans<\/span><span class=\"result-term\">\u03c3\u00b2<\/span><\/span><span class=\"field-value\" id=\"result-6\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-7\"><span class=\"field-title\"><span>Standart sapma<\/span><span class=\"result-term\">\u03c3<\/span><\/span><span class=\"field-value\" id=\"result-7\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-8\"><span class=\"field-title\"><span>Yorum ve ayr\u0131nt\u0131lar<\/span><\/span><span class=\"field-value\" id=\"result-8\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Bu hesaplaman\u0131n ba\u011flant\u0131s\u0131n\u0131 kopyala<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Yorum b\u0131rak<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"852\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Bu sonu\u00e7 hakk\u0131nda ne d\u00fc\u015f\u00fcn\u00fcyorsunuz?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Be\u011fendim <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Faydal\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Kafam kar\u0131\u015ft\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Hayal k\u0131r\u0131kl\u0131\u011f\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Hatal\u0131 <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Binom Da\u011f\u0131l\u0131m\u0131 Form\u00fcl\u00fc<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Form\u00fcl<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ P(X = k) = \\binom{n}{k} p^k (1-p)^{n-k}, \\qquad \\binom{n}{k} = \\frac{n!}{k!\\,(n-k)!} \\\\ P(X \\le k) = \\sum_{i=0}^{k} \\binom{n}{i} p^i (1-p)^{n-i}, \\qquad P(X \\ge k) = 1 - P(X \\le k-1) \\\\ \\mu = np, \\qquad \\sigma^2 = np(1-p), \\qquad \\sigma = \\sqrt{np(1-p)} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Buradaki g\u00f6sterimler:<\/strong><\/p>\n<ul>\n<li>\\(n\\) \u2014 ba\u011f\u0131ms\u0131z deneme say\u0131s\u0131<\/li>\n<li>\\(p\\) \u2014 tek bir denemede ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 (0 ile 1 aras\u0131nda)<\/li>\n<li>\\(k\\) \u2014 ilgilenilen ba\u015far\u0131 say\u0131s\u0131 (\\(0 \\le k \\le n\\))<\/li>\n<li>\\(\\binom{n}{k}\\) \u2014 binom katsay\u0131s\u0131, \\(n\\) deneme aras\u0131ndan \\(k\\) ba\u015far\u0131 se\u00e7me yollar\u0131n\u0131n say\u0131s\u0131<\/li>\n<li>\\(\\mu\\), \\(\\sigma^2\\), \\(\\sigma\\) \u2014 da\u011f\u0131l\u0131m\u0131n ortalamas\u0131, varyans\u0131 ve standart sapmas\u0131<\/li>\n<\/ul>\n<p>\u0130lk form\u00fcl olas\u0131l\u0131k k\u00fctle fonksiyonunu (pmf) verir: \\(n\\) denemede tam olarak \\(k\\) ba\u015far\u0131 elde etme \u015fans\u0131. \u0130kincisi k\u00fcm\u00fclatif da\u011f\u0131l\u0131m fonksiyonunu (cdf) verir; yani en fazla \\(k\\) ba\u015far\u0131 elde etme \u015fans\u0131, pmf'nin 0'dan \\(k\\)'ya toplanmas\u0131yla bulunur.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Binom Da\u011f\u0131l\u0131m\u0131 \u2013 Hesaplama \u00d6rne\u011fi<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> adil bir para 10 kez at\u0131l\u0131yor. Tam olarak 5 kez yaz\u0131 gelme olas\u0131l\u0131\u011f\u0131 nedir? Burada \\(n = 10\\), \\(p = 0.5\\), \\(k = 5\\).<\/p>\n<p>\\[ P(X = 5) = \\binom{10}{5} (0.5)^5 (0.5)^{10-5} = 252 \\cdot \\frac{1}{1024} = 0.246094 \\approx 24.61\\% \\]<\/p>\n<p>\\[ P(X \\le 5) = \\sum_{i=0}^{5} \\binom{10}{i}(0.5)^{10} = \\frac{638}{1024} = 0.623047 \\approx 62.30\\% \\]<\/p>\n<p>\\[ \\mu = 10 \\cdot 0.5 = 5, \\qquad \\sigma^2 = 10 \\cdot 0.5 \\cdot 0.5 = 2.5, \\qquad \\sigma = \\sqrt{2.5} \\approx 1.5811 \\]<\/p>\n<p><strong>Sonu\u00e7:<\/strong> P(X = 5) = 0.246094 (%24,61), P(X \u2264 5) = 0.623047 (%62,30), P(X \u2265 5) = 0.623047 (%62,30), ortalama = 5, varyans = 2.5, standart sapma \u2248 1.5811.<\/p>\n<p>\n\r\n<\/section>\n<h2>Hesaplama arac\u0131 nas\u0131l kullan\u0131l\u0131r?<\/h2>\n<ol>\n<li><strong>Deneme say\u0131s\u0131n\u0131 (n)<\/strong> girin \u2014 1 ile 10.000 aras\u0131nda bir tam say\u0131.<\/li>\n<li><strong>Ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131n\u0131 (p)<\/strong> %0 ile %100 aras\u0131nda bir y\u00fczde olarak girin (\u00f6rne\u011fin adil bir para i\u00e7in 50 girin).<\/li>\n<li><strong>\u0130lgilenilen ba\u015far\u0131lar<\/strong> alt\u0131nda modu se\u00e7in: tek bir de\u011fer i\u00e7in \u201cTam olarak k ba\u015far\u0131\u201d, bir aral\u0131k i\u00e7in \u201ck\u2081 ile k\u2082 aras\u0131 ba\u015far\u0131\u201d.<\/li>\n<li><strong>Ba\u015far\u0131 say\u0131s\u0131n\u0131 (k)<\/strong> girin. Aral\u0131k modunda bu, alt s\u0131n\u0131r olan k\u2081'dir.<\/li>\n<li>Aral\u0131k modunu se\u00e7tiyseniz ayr\u0131ca en az k\u2081 olmas\u0131 gereken <strong>\u00dcst s\u0131n\u0131r\u0131 (k\u2082)<\/strong> girin.<\/li>\n<li>Sonu\u00e7lar\u0131 okuyun: P(X = k), P(X \u2264 k), P(X \u2265 k) ve aral\u0131k modunda P(k\u2081 \u2264 X \u2264 k\u2082), ayr\u0131ca ortalama, varyans ve standart sapma. Yorumlama b\u00f6l\u00fcm\u00fcnde P(X &lt; k) ve P(X &gt; k) gibi tamamlay\u0131c\u0131 olas\u0131l\u0131klar da listelenir.<\/li>\n<\/ol>\n<h2>Binom da\u011f\u0131l\u0131m\u0131 nedir?<\/h2>\n<p>Binom da\u011f\u0131l\u0131m\u0131, her denemenin ayn\u0131 ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131na \\(p\\) sahip oldu\u011fu, sabit say\u0131da ba\u011f\u0131ms\u0131z denemedeki ba\u015far\u0131 say\u0131s\u0131n\u0131 modeller. Her denemenin tam olarak iki sonucu vard\u0131r \u2014 ba\u015far\u0131 veya ba\u015far\u0131s\u0131zl\u0131k \u2014 bu y\u00fczden buna Bernoulli denemesi denir. Klasik \u00f6rnekler aras\u0131nda bir dizi para at\u0131\u015f\u0131nda yaz\u0131 gelme say\u0131s\u0131, bir \u00f6rnekteki hatal\u0131 \u00fcr\u00fcn say\u0131s\u0131 veya bir tedaviye yan\u0131t veren hasta say\u0131s\u0131 yer al\u0131r.<\/p>\n<p>Da\u011f\u0131l\u0131m\u0131n ortalamas\u0131 \\(\\mu = np\\)'dir: ortalama olarak \\(n \\cdot p\\) ba\u015far\u0131 beklenir. Yay\u0131l\u0131m, varyans \\(\\sigma^2 = np(1-p)\\) ve standart sapma \\(\\sigma\\) ile \u00f6l\u00e7\u00fcl\u00fcr. \\(p = 0.5\\) oldu\u011funda da\u011f\u0131l\u0131m \\(n\/2\\) etraf\u0131nda simetriktir; \\(p\\) 0'a veya 1'e yak\u0131n oldu\u011funda ise \u00e7arp\u0131kla\u015f\u0131r ve 0 civar\u0131nda ya da \\(n\\) civar\u0131nda y\u0131\u011f\u0131l\u0131r.<\/p>\n<p>Hesaplama arac\u0131 kesin ve k\u00fcm\u00fclatif olas\u0131l\u0131klar\u0131 birbirinden ay\u0131r\u0131r. Olas\u0131l\u0131k k\u00fctle fonksiyonu \u201ctam olarak k ba\u015far\u0131 \u015fans\u0131 nedir\u201d sorusunu, k\u00fcm\u00fclatif da\u011f\u0131l\u0131m fonksiyonu ise \u201cen fazla k ba\u015far\u0131 \u015fans\u0131 nedir\u201d sorusunu yan\u0131tlar. K\u00fcm\u00fclatif de\u011ferler pratikte \u00e7o\u011fu zaman daha kullan\u0131\u015fl\u0131d\u0131r: \u00f6rne\u011fin k bir kalite e\u015fi\u011fiyse, P(X \u2264 k) s\u0131n\u0131r i\u00e7inde kalma olas\u0131l\u0131\u011f\u0131n\u0131, 1 \u2212 P(X \u2264 k) ise s\u0131n\u0131r\u0131 a\u015fma olas\u0131l\u0131\u011f\u0131n\u0131 verir. P(X \u2265 k)'n\u0131n k'n\u0131n kendisini de i\u00e7erdi\u011fini unutmay\u0131n; kesin olarak k'dan fazlas\u0131na ihtiyac\u0131n\u0131z varsa, yorumlama b\u00f6l\u00fcm\u00fcnde g\u00f6sterilen P(X &gt; k) = 1 \u2212 P(X \u2264 k) de\u011ferini kullan\u0131n.<\/p>\n<h2>Varsay\u0131mlar, s\u0131n\u0131rlamalar ve ipu\u00e7lar\u0131<\/h2>\n<ul>\n<li><strong>Sabit deneme say\u0131s\u0131.<\/strong> \\(n\\) \u00f6nceden belirlenmi\u015f olmal\u0131d\u0131r. Deneme say\u0131s\u0131n\u0131n kendisi rastgelese, farkl\u0131 bir model (\u00f6rne\u011fin Poisson da\u011f\u0131l\u0131m\u0131) daha uygundur.<\/li>\n<li><strong>Ba\u011f\u0131ms\u0131zl\u0131k.<\/strong> Bir denemenin sonucu di\u011ferini etkilememelidir. K\u00fc\u00e7\u00fck bir pop\u00fclasyondan geri koymadan \u00f6rnekleme bunu ihlal eder; bunun yerine hipergeometrik da\u011f\u0131l\u0131m\u0131 kullan\u0131n.<\/li>\n<li><strong>Sabit ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131.<\/strong> \\(p\\) her deneme i\u00e7in ayn\u0131 olmal\u0131d\u0131r. Denemeden denemeye de\u011fi\u015fiyorsa binom model art\u0131k ge\u00e7erli de\u011fildir.<\/li>\n<li><strong>B\u00fcy\u00fck n.<\/strong> Hesaplama arac\u0131 say\u0131sal olarak kararl\u0131 bir log-gamma y\u00f6ntemi kullan\u0131r, bu nedenle b\u00fcy\u00fck \\(n\\) de\u011ferlerini (10.000'e kadar) ta\u015fma olmadan i\u015fler. \u00c7ok k\u00fc\u00e7\u00fck olas\u0131l\u0131klar i\u00e7in sonu\u00e7 bilimsel g\u00f6sterimle g\u00f6sterilir.<\/li>\n<li><strong>\u00c7ok k\u00fc\u00e7\u00fck olas\u0131l\u0131klar\u0131n yorumlanmas\u0131.<\/strong> \u201c\u2248 %0\u201d gibi bir sonu\u00e7 imk\u00e2ns\u0131z oldu\u011fu anlam\u0131na gelmez \u2014 yaln\u0131zca olas\u0131l\u0131\u011f\u0131n yakla\u015f\u0131k \\(10^{-8}\\)'den k\u00fc\u00e7\u00fck olabilece\u011fi anlam\u0131na gelir. Y\u00fczdenin yan\u0131nda g\u00f6sterilen ondal\u0131k de\u011feri kontrol edin.<\/li>\n<li><strong>Yakla\u015f\u0131m i\u00e7in pratik kural.<\/strong> \\(np\\) ve \\(n(1-p)\\)'nin her ikisinin de yakla\u015f\u0131k 5'ten b\u00fcy\u00fck oldu\u011fu b\u00fcy\u00fck \\(n\\) de\u011ferlerinde, binom da\u011f\u0131l\u0131m\u0131 ortalamas\u0131 \\(np\\) ve standart sapmas\u0131 \\(\\sqrt{np(1-p)}\\) olan bir normal da\u011f\u0131l\u0131mla iyi bir \u015fekilde yakla\u015f\u0131labilir \u2014 h\u0131zl\u0131 zihinsel tahminler i\u00e7in kullan\u0131\u015fl\u0131d\u0131r.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Binom olas\u0131l\u0131klar\u0131n\u0131 hesaplay\u0131n: P(X = k), k\u00fcm\u00fclatif P(X \u2264 k), P(X \u2265 k) veya bir ba\u015far\u0131 aral\u0131\u011f\u0131. Deneme say\u0131s\u0131n\u0131, ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131n\u0131 ve k de\u011ferini girerek ortalama, varyans ve standart sapmay\u0131 da elde edin.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[12],"tags":[34],"class_list":["post-852","post","type-post","status-publish","format-standard","hentry","category-istatistik","tag-dagilimlar"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/852","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/comments?post=852"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/852\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=852"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=852"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=852"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}