{"id":864,"date":"2026-10-03T18:04:11","date_gmt":"2026-10-03T17:04:11","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/hipergeometrik-dagilim-hesaplayici\/"},"modified":"2026-10-03T18:04:11","modified_gmt":"2026-10-03T17:04:11","slug":"hipergeometrik-dagilim-hesaplayici","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/istatistik\/hipergeometrik-dagilim-hesaplayici\/","title":{"rendered":"Hipergeometrik Da\u011f\u0131l\u0131m Hesaplay\u0131c\u0131s\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\">Hipergeometrik Olas\u0131l\u0131klar\u0131 Hesaplay\u0131n<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"864\" data-favorite-title=\"Hipergeometrik Da\u011f\u0131l\u0131m\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/istatistik\/hipergeometrik-dagilim-hesaplayici\/\" data-favorite-excerpt=\"Yerine koymadan \u00f6rnekleme i\u00e7in kesin ve k\u00fcm\u00fclatif hipergeometrik olas\u0131l\u0131klar\u0131 hesaplay\u0131n. Pop\u00fclasyon b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fc, ba\u015far\u0131 say\u0131s\u0131n\u0131, \u00e7ekili\u015f say\u0131s\u0131n\u0131 ve istenen ba\u015far\u0131 say\u0131s\u0131n\u0131 girin.\" 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\/hipergeometrik-dagilim-hesaplayici\/\" method=\"POST\" class=\"calculator\" id=\"calculator-864\" data-post=\"864\"><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\">Pop\u00fclasyon b\u00fcy\u00fckl\u00fc\u011f\u00fc<\/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=\"poplasyon_bykl\" id=\"field-1\" aria-describedby=\"calc-unit-1 calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"1\" value=\"52\"\/><div class=\"unit\" id=\"calc-unit-1\">\u00f6\u011fe<\/div><small id=\"calc-info-1\">Pop\u00fclasyondaki toplam \u00f6\u011fe say\u0131s\u0131.<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Pop\u00fclasyondaki ba\u015far\u0131 say\u0131s\u0131<\/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=\"poplasyondaki_baar_says\" id=\"field-2\" aria-describedby=\"calc-unit-2 calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"13\"\/><div class=\"unit\" id=\"calc-unit-2\">\u00f6\u011fe<\/div><small id=\"calc-info-2\">Pop\u00fclasyonda istenen \u00f6zelli\u011fe sahip \u00f6\u011felerin say\u0131s\u0131.<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">\u00c7ekim say\u0131s\u0131 (\u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc)<\/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=\"ekim_says_rneklem_bykl\" id=\"field-3\" aria-describedby=\"calc-unit-3 calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"5\"\/><div class=\"unit\" id=\"calc-unit-3\">\u00e7ekim<\/div><small id=\"calc-info-3\">Geri koymadan \u00e7ekilen \u00f6\u011fe say\u0131s\u0131.<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">\u0130stenen ba\u015far\u0131 say\u0131s\u0131<\/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=\"stenen_baar_says\" id=\"field-4\" aria-describedby=\"calc-unit-4 calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"2\"\/><div class=\"unit\" id=\"calc-unit-4\">ba\u015far\u0131<\/div><small id=\"calc-info-4\">\u00c7ekimler aras\u0131nda istedi\u011finiz ba\u015far\u0131 say\u0131s\u0131.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"864\">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> Hipergeometrik Olas\u0131l\u0131klar<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Kesin olas\u0131l\u0131k P(X = k)<\/span><\/span><span class=\"field-value\" id=\"result-1\" data-unit=\"%\"><\/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>K\u00fcm\u00fclatif P(X \u2264 k)<\/span><\/span><span class=\"field-value\" id=\"result-2\" data-unit=\"%\"><\/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>K\u00fcm\u00fclatif P(X &lt; k)<\/span><\/span><span class=\"field-value\" id=\"result-3\" data-unit=\"%\"><\/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>K\u00fcm\u00fclatif P(X \u2265 k)<\/span><\/span><span class=\"field-value\" id=\"result-4\" data-unit=\"%\"><\/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>K\u00fcm\u00fclatif P(X &gt; k)<\/span><\/span><span class=\"field-value\" id=\"result-5\" data-unit=\"%\"><\/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-6\"><span class=\"field-title\"><span>Ortalama ve standart sapma<\/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 is-column\" id=\"output-7\"><span class=\"field-title\"><span>De\u011ferlerinizle form\u00fcl<\/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<\/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=\"864\" 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>Hipergeometrik Da\u011f\u0131l\u0131m 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) = \\frac{\\binom{K}{k}\\binom{N-K}{n-k}}{\\binom{N}{n}} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Burada:<\/strong><\/p>\n<ul>\n<li>\\(N\\) \u2014 pop\u00fclasyon b\u00fcy\u00fckl\u00fc\u011f\u00fc (toplam nesne say\u0131s\u0131)<\/li>\n<li>\\(K\\) \u2014 pop\u00fclasyondaki ba\u015far\u0131 say\u0131s\u0131 (istenen \u00f6zelli\u011fe sahip nesneler)<\/li>\n<li>\\(n\\) \u2014 \u00e7ekili\u015f say\u0131s\u0131 (\u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc, yerine koymadan \u00e7ekilir)<\/li>\n<li>\\(k\\) \u2014 \u00f6rneklemede istenen ba\u015far\u0131 say\u0131s\u0131<\/li>\n<\/ul>\n<p>Bu form\u00fcl, \\(K\\) ba\u015far\u0131 i\u00e7eren \\(N\\) nesnelilik sonlu bir pop\u00fclasyondan yerine koymadan \u00e7ekilen \\(n\\) nesnelik bir \u00f6rneklemede tam olarak \\(k\\) ba\u015far\u0131 bulunma olas\u0131l\u0131\u011f\u0131n\u0131 verir. Ortalama ve standart sapma \\(E(X) = nK\/N\\) ve \\(SD(X) = \\sqrt{n \\cdot \\frac{K}{N} \\cdot \\left(1 - \\frac{K}{N}\\right) \\cdot \\frac{N-n}{N-1}}\\) \u015feklindedir.<\/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>Hipergeometrik Da\u011f\u0131l\u0131m \u2013 Hesaplama \u00d6rne\u011fi<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> standart bir iskambil destesinde 52 kart vard\u0131r ve bunlar\u0131n 13'\u00fc kupa (ma\u00e7a de\u011fil, kupa de\u011fil \u2014 hearts) y\u00f6n\u00fcnden de\u011fil, \u00abkupa\u00bb yerine \u00abkupa\u00bb diyelim: standart bir destede 52 kart vard\u0131r, 13'\u00fc kuptur. 5 kart \u00e7ekiyorsunuz ve tam 2 kup alma olas\u0131l\u0131\u011f\u0131n\u0131 istiyorsunuz. Yani \\(N = 52\\), \\(K = 13\\), \\(n = 5\\), \\(k = 2\\).<\/p>\n<p>\\[ P(X = 2) = \\frac{\\binom{13}{2}\\binom{39}{3}}{\\binom{52}{5}} = \\frac{78 \\times 9139}{2598960} = \\frac{712842}{2598960} \\approx 0.2743 \\]<\/p>\n<p><strong>Sonu\u00e7:<\/strong> \\(P(X = 2) \\approx 0.2743\\), yani yakla\u015f\u0131k %27,43 (kabaca 4'te 1). K\u00fcm\u00fclatif olas\u0131l\u0131k \\(P(X \\le 2)\\) yakla\u015f\u0131k %90,72, ortalama \\(E(X) = 1.25\\) kup ve standart sapma yakla\u015f\u0131k 0,93't\u00fcr.<\/p>\n<p>\n\r\n<\/section>\n<h2>Hesaplay\u0131c\u0131 Nas\u0131l Kullan\u0131l\u0131r?<\/h2>\n<ol>\n<li><strong>Pop\u00fclasyon b\u00fcy\u00fckl\u00fc\u011f\u00fc<\/strong> \\(N\\) de\u011ferini girin \u2014 i\u00e7inden \u00e7ekim yapt\u0131\u011f\u0131n\u0131z toplam nesne say\u0131s\u0131.<\/li>\n<li><strong>Pop\u00fclasyondaki ba\u015far\u0131 say\u0131s\u0131<\/strong> \\(K\\) de\u011ferini girin \u2014 bu nesnelerden ka\u00e7 tanesinin ilgilendi\u011finiz \u00f6zelli\u011fe sahip oldu\u011fu.<\/li>\n<li><strong>\u00c7ekili\u015f say\u0131s\u0131 (\u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc)<\/strong> \\(n\\) de\u011ferini girin \u2014 yerine koymadan ka\u00e7 nesne \u00e7ekti\u011finiz.<\/li>\n<li><strong>\u0130stenen ba\u015far\u0131 say\u0131s\u0131<\/strong> \\(k\\) de\u011ferini girin \u2014 \u00f6rnekleminizde istedi\u011finiz ba\u015far\u0131 say\u0131s\u0131.<\/li>\n<li>Sonu\u00e7lar\u0131 okuyun: kesin olas\u0131l\u0131k \\(P(X = k)\\), k\u00fcm\u00fclatif olas\u0131l\u0131klar \\(P(X \\le k)\\), \\(P(X  k)\\) (t\u00fcm\u00fc y\u00fczde olarak), ayr\u0131ca ortalama, standart sapma, de\u011ferlerinizin yerle\u015ftirildi\u011fi form\u00fcl ve sade bir dille a\u00e7\u0131klama.<\/li>\n<\/ol>\n<h2>Hipergeometrik Da\u011f\u0131l\u0131m Nedir?<\/h2>\n<p>Hipergeometrik da\u011f\u0131l\u0131m, sonlu bir pop\u00fclasyondan sabit say\u0131da nesneyi <em>yerine koymadan<\/em> \u00e7ekti\u011finizde elde etti\u011finiz ba\u015far\u0131 say\u0131s\u0131n\u0131 tan\u0131mlar. Her \u00e7ekimin geriye kalanlar\u0131n bile\u015fimini de\u011fi\u015ftirdi\u011fi her durumda do\u011fru modeldir \u2014 desteden kart da\u011f\u0131tmak, kalite kontrol\u00fc i\u00e7in bir partiden par\u00e7a se\u00e7mek, k\u00fc\u00e7\u00fck bir gruptan ankete ki\u015fi se\u00e7mek veya piyango numaralar\u0131 \u00e7ekmek.<\/p>\n<p>En yak\u0131n akrabas\u0131 binom da\u011f\u0131l\u0131m\u0131d\u0131r; o, nesnelerin <em>yerine koyarak<\/em> \u00e7ekildi\u011fi (veya etkin bi\u00e7imde sonsuz bir pop\u00fclasyondan \u00e7ekildi\u011fi) durumlarda ge\u00e7erlidir, bu y\u00fczden her denemede ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 ayn\u0131d\u0131r. Hipergeometrik da\u011f\u0131l\u0131mda ise her kald\u0131rd\u0131\u011f\u0131n\u0131z ba\u015far\u0131, kalan \u00e7ekili\u015fler i\u00e7in ba\u015far\u0131 oran\u0131n\u0131 d\u00fc\u015f\u00fcr\u00fcr \u2014 ger\u00e7ek bir iskambil destesinde veya sonlu bir \u00fcr\u00fcn partisinde tam olarak ger\u00e7ekle\u015fen durum budur. \u00d6rneklem pop\u00fclasyona k\u0131yasla k\u00fc\u00e7\u00fckse (\u00f6rne\u011fin %5\u201310'un alt\u0131ndaysa), iki da\u011f\u0131l\u0131m neredeyse ayn\u0131 sonu\u00e7lar\u0131 verir.<\/p>\n<p>Hesaplay\u0131c\u0131 t\u00fcm olas\u0131 sonu\u00e7lar\u0131n olas\u0131l\u0131klar\u0131n\u0131 ayn\u0131 anda raporlar; bu \u00e7o\u011fu zaman tek bir kesin de\u011ferden daha kullan\u0131\u015fl\u0131d\u0131r. \u00d6rne\u011fin bir kalite denet\u00e7isi \\(P(X \\ge k)\\) de\u011ferine \u2014 belirli say\u0131da hatal\u0131 par\u00e7a bulma <em>\u015fans\u0131n\u0131n en az<\/em> ne kadar oldu\u011funa \u2014 ihtiya\u00e7 duyarken, bir kart oyuncusu \\(P(X \\le k)\\) de\u011ferini, yani birka\u00e7 anahtar kart\u0131 <em>en fazla<\/em> \u00e7ekme \u015fans\u0131n\u0131 isteyebilir. Ortalama \\(E(X) = nK\/N\\), ortalama bir \u00f6rneklemede beklenen ba\u015far\u0131 say\u0131s\u0131n\u0131 s\u00f6yler; basit\u00e7e \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn pop\u00fclasyon ba\u015far\u0131 oran\u0131yla \u00e7arp\u0131m\u0131d\u0131r.<\/p>\n<p>Da\u011f\u0131l\u0131m\u0131n bi\u00e7imi parametrelere ba\u011fl\u0131d\u0131r: simetrik, az say\u0131da ba\u015far\u0131ya do\u011fru \u00e7arp\u0131k veya \u00e7ok say\u0131da ba\u015far\u0131ya do\u011fru \u00e7arp\u0131k olabilir. \\(X\\) de\u011ferleri de s\u0131n\u0131rl\u0131d\u0131r \u2014 pop\u00fclasyonda var olan ba\u015far\u0131 say\u0131s\u0131ndan veya \u00e7ekti\u011finiz nesne say\u0131s\u0131ndan daha fazla ba\u015far\u0131 \u00e7ekemezsiniz; dolay\u0131s\u0131yla ba\u015far\u0131 say\u0131s\u0131 \\([\\max(0, n-(N-K)), \\; \\min(n, K)]\\) aral\u0131\u011f\u0131yla s\u0131n\u0131rl\u0131d\u0131r. Hesaplay\u0131c\u0131, \\(k\\) de\u011feriniz bu aral\u0131\u011f\u0131n d\u0131\u015f\u0131ndaysa otomatik olarak s\u0131f\u0131r olas\u0131l\u0131\u011f\u0131 d\u00f6nd\u00fcr\u00fcr.<\/p>\n<h2>Varsay\u0131mlar, S\u0131n\u0131rlamalar ve \u0130pu\u00e7lar\u0131<\/h2>\n<ul>\n<li><strong>Yerine koymadan \u00f6rnekleme:<\/strong> model, \u00e7ekilen nesnelerin pop\u00fclasyona geri konulmad\u0131\u011f\u0131n\u0131 varsayar. Nesneler her \u00e7ekimden sonra geri konuluyorsa, bunun yerine <a href=\"https:\/\/wpcalc.com\/tr\/istatistik\/binom-dagilimi-hesaplama\/\">Binom Da\u011f\u0131l\u0131m Hesaplay\u0131c\u0131s\u0131n\u0131<\/a> kullan\u0131n.<\/li>\n<li><strong>Sabit \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc:<\/strong> \u00e7ekili\u015f say\u0131s\u0131 \\(n\\) \u00f6nceden belirlenmeli ve sabit kalmal\u0131d\u0131r. Sabit bir zaman veya mek\u00e2n aral\u0131\u011f\u0131nda rastgele ger\u00e7ekle\u015fen olaylar\u0131 say\u0131yorsan\u0131z, <a href=\"https:\/\/wpcalc.com\/tr\/istatistik\/poisson-dagilimi-hesaplama\/\">Poisson Da\u011f\u0131l\u0131m Hesaplay\u0131c\u0131s\u0131<\/a> daha uygun bir ara\u00e7t\u0131r.<\/li>\n<li><strong>E\u015fit olas\u0131l\u0131kl\u0131 \u00f6rnekler:<\/strong> \\(n\\) nesnenin her olas\u0131 alt k\u00fcmesinin \u00e7ekilme \u015fans\u0131 ayn\u0131 olmal\u0131d\u0131r. Baz\u0131 nesnelerin se\u00e7ilme olas\u0131l\u0131\u011f\u0131 daha y\u00fcksekse hipergeometrik model ge\u00e7erli olmaz.<\/li>\n<li><strong>Yaln\u0131zca tam say\u0131lar:<\/strong> \\(N\\), \\(K\\), \\(n\\) ve \\(k\\) tam say\u0131 olmal\u0131d\u0131r; \\(1 \\le N \\le 1{,}000{,}000\\), \\(0 \\le K \\le N\\), \\(0 \\le n \\le N\\) ve \\(0 \\le k \\le n\\) ko\u015fullar\u0131 sa\u011flanmal\u0131d\u0131r.<\/li>\n<li><strong>B\u00fcy\u00fck pop\u00fclasyonlar:<\/strong> \\(n\\), \\(N\\)'ye k\u0131yasla k\u00fc\u00e7\u00fck oldu\u011funda hipergeometrik da\u011f\u0131l\u0131m, binom da\u011f\u0131l\u0131m\u0131yla (veya b\u00fcy\u00fck say\u0131lar i\u00e7in <a href=\"https:\/\/wpcalc.com\/tr\/istatistik\/normal-dagilim-hesaplayici\/\">normal da\u011f\u0131l\u0131mla<\/a>) iyi bir \u015fekilde yakla\u015f\u0131k hesaplanabilir; ancak bu hesaplay\u0131c\u0131 herhangi bir yakla\u015f\u0131kl\u0131\u011fa gerek duymadan kesin sonucu verir.<\/li>\n<li><strong>Binom katsay\u0131lar\u0131n\u0131 kontrol edin:<\/strong> de\u011ferlerin yerle\u015ftirildi\u011fi form\u00fcl \\(\\binom{a}{b}\\) g\u00f6sterimini kullan\u0131r. Bu de\u011ferleri <a href=\"https:\/\/wpcalc.com\/tr\/istatistik\/permutasyon-kombinasyon-hesaplayici\/\">Permutasyon ve Kombinasyon Hesaplay\u0131c\u0131s\u0131yla<\/a> do\u011frulayabilirsiniz.<\/li>\n<li><strong>S\u0131f\u0131r olas\u0131l\u0131\u011f\u0131 yorumlama:<\/strong> %0 sonucu genellikle \\(k\\) de\u011ferinizin olanaks\u0131z oldu\u011fu anlam\u0131na gelir \u2014 \u00f6rne\u011fin pop\u00fclasyonda yaln\u0131zca 2 ba\u015far\u0131 nesnesi varken 3 ba\u015far\u0131 istemek.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Yerine koymadan \u00f6rnekleme i\u00e7in kesin ve k\u00fcm\u00fclatif hipergeometrik olas\u0131l\u0131klar\u0131 hesaplay\u0131n. Pop\u00fclasyon b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fc, ba\u015far\u0131 say\u0131s\u0131n\u0131, \u00e7ekili\u015f say\u0131s\u0131n\u0131 ve istenen ba\u015far\u0131 say\u0131s\u0131n\u0131 girin.<\/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-864","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\/864","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=864"}],"version-history":[{"count":2,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/864\/revisions"}],"predecessor-version":[{"id":3695,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/864\/revisions\/3695"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=864"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=864"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=864"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}