{"id":359,"date":"2026-10-03T13:58:40","date_gmt":"2026-10-03T12:58:40","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/ustel-dagilim-hesaplayici\/"},"modified":"2026-10-03T13:58:40","modified_gmt":"2026-10-03T12:58:40","slug":"ustel-dagilim-hesaplayici","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/istatistik\/ustel-dagilim-hesaplayici\/","title":{"rendered":"\u00dcstel Da\u011f\u0131l\u0131m Hesaplay\u0131c\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\">\u00dcstel Da\u011f\u0131l\u0131m 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=\"359\" data-favorite-title=\"\u00dcstel Da\u011f\u0131l\u0131m\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/istatistik\/ustel-dagilim-hesaplayici\/\" data-favorite-excerpt=\"Oran \u03bb veya ortalama bekleme s\u00fcresiyle \u00fcstel da\u011f\u0131l\u0131m olas\u0131l\u0131klar\u0131n\u0131 hesaplay\u0131n: yo\u011funluk, P(X \u2264 t), P(X &gt; t), aral\u0131k olas\u0131l\u0131\u011f\u0131, ortalama ve medyan. Oran\u0131, bir s\u00fcreyi ve iste\u011fe ba\u011fl\u0131 bir aral\u0131k sonunu 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\/ustel-dagilim-hesaplayici\/\" method=\"POST\" class=\"calculator\" id=\"calculator-359\" data-post=\"359\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Giri\u015f alanlar\u0131<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">Parametreyi belirleme y\u00f6ntemi<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"parametreyi_belirleme_yntemi\"><option value=\"rate\" selected>H\u0131z \u03bb (birim zamandaki olay)<\/option><option value=\"mean\">Ortalama bekleme s\u00fcresi \u03bc<\/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-2\"><label for=\"field-2\">H\u0131z (\u03bb)<\/label><div class=\"term\">\u03bb<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"hz_\" id=\"field-2\" aria-describedby=\"calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"2\"\/><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"zaman_birimi\" aria-label=\"zaman birimi\"><option value=\"1\">saniye ba\u015f\u0131na<\/option><option value=\"60\">dakika ba\u015f\u0131na<\/option><option value=\"3600\" selected>saat ba\u015f\u0131na<\/option><option value=\"86400\">g\u00fcn ba\u015f\u0131na<\/option><option value=\"31536000\">y\u0131l ba\u015f\u0131na<\/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><small id=\"calc-info-2\">Birim zamandaki ortalama olay say\u0131s\u0131.<\/small><\/div><div class=\"field has-term\" id=\"input-3\" hidden><label for=\"field-4\">Ortalama bekleme s\u00fcresi (\u03bc)<\/label><div class=\"term\">\u03bc<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"ortalama_bekleme_sresi_\" id=\"field-4\" aria-describedby=\"calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"30\"\/><div class=\"grid grid-cols-1\"><select id=\"field-5\" name=\"birim\" aria-label=\"birim\"><option value=\"1\">saniye<\/option><option value=\"60\" selected>dakika<\/option><option value=\"3600\">saat<\/option><option value=\"86400\">g\u00fcn<\/option><option value=\"31536000\">y\u0131l<\/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><small id=\"calc-info-4\">Ard\u0131\u015f\u0131k olaylar aras\u0131ndaki ortalama s\u00fcre (\u03bb = 1\/\u03bc).<\/small><\/div><div class=\"is-single field\" id=\"input-4\"><span class=\"font-semibold\">S\u00fcre<\/span><\/div><div class=\"field has-term\" id=\"input-5\"><label for=\"field-7\">S\u00fcre (t)<\/label><div class=\"term\">t<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"sre_t\" id=\"field-7\" aria-describedby=\"calc-info-7\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"1\"\/><div class=\"grid grid-cols-1\"><select id=\"field-8\" name=\"birim\" aria-label=\"birim\"><option value=\"1\">saniye<\/option><option value=\"60\">dakika<\/option><option value=\"3600\" selected>saat<\/option><option value=\"86400\">g\u00fcn<\/option><option value=\"31536000\">y\u0131l<\/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><small id=\"calc-info-7\">\u0130lgilendi\u011finiz bekleme s\u00fcresi.<\/small><\/div><div class=\"field has-term\" id=\"input-6\"><label for=\"field-9\">Aral\u0131k sonu (b)<\/label><div class=\"term\">b<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"aralk_sonu_b\" id=\"field-9\" aria-describedby=\"calc-info-9\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"2\"\/><div class=\"grid grid-cols-1\"><select id=\"field-10\" name=\"birim\" aria-label=\"birim\"><option value=\"1\">saniye<\/option><option value=\"60\">dakika<\/option><option value=\"3600\" selected>saat<\/option><option value=\"86400\">g\u00fcn<\/option><option value=\"31536000\">y\u0131l<\/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><small id=\"calc-info-9\">\u0130ste\u011fe ba\u011fl\u0131: P(t \u2264 X \u2264 b) de\u011ferini de almak i\u00e7in doldurun. Atlamak i\u00e7in bo\u015f b\u0131rak\u0131n.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"359\">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> \u00dcstel Da\u011f\u0131l\u0131m Sonu\u00e7lar\u0131<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Yo\u011funluk f(t)<\/span><span class=\"result-term\">f(t)<\/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>K\u00fcm\u00fclatif olas\u0131l\u0131k P(X \u2264 t)<\/span><span class=\"result-term\">F(t)<\/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>Sa\u011fkal\u0131m olas\u0131l\u0131\u011f\u0131 P(X &gt; t)<\/span><span class=\"result-term\">S(t)<\/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>Aral\u0131k olas\u0131l\u0131\u011f\u0131 P(t \u2264 X \u2264 b)<\/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>Ortalama bekleme s\u00fcresi E(X)<\/span><span class=\"result-term\">E(X)<\/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 is-column\" id=\"output-6\"><span class=\"field-title\"><span>Form\u00fcl, medyan ve yorum<\/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><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=\"359\" 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>\u00dcstel 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\\[ f(t) = \\lambda e^{-\\lambda t}, \\qquad F(t) = P(X \\le t) = 1 - e^{-\\lambda t} \\]\n\\[ S(t) = P(X &gt; t) = e^{-\\lambda t}, \\qquad P(a \\le X \\le b) = e^{-\\lambda a} - e^{-\\lambda b} \\]\n\\[ E(X) = \\frac{1}{\\lambda}, \\qquad \\text{medyan} = \\frac{\\ln 2}{\\lambda} \\]<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Burada:<\/strong><\/p>\n<ul>\n<li>\\(\\lambda\\) \u2014 oran parametresi: birim zamanda ger\u00e7ekle\u015fen ortalama olay say\u0131s\u0131<\/li>\n<li>\\(t\\) \u2014 ilgilenilen bekleme s\u00fcresi<\/li>\n<li>\\(f(t)\\) \u2014 \\(t\\) an\u0131ndaki olas\u0131l\u0131k yo\u011funlu\u011fu<\/li>\n<li>\\(F(t)\\) \u2014 \\(t\\) s\u00fcresinden uzun beklememe (k\u00fcm\u00fclatif) olas\u0131l\u0131\u011f\u0131<\/li>\n<li>\\(S(t)\\) \u2014 \\(t\\) s\u00fcresinden uzun bekleme (sa\u011fkal\u0131m) olas\u0131l\u0131\u011f\u0131<\/li>\n<\/ul>\n<p>\u00dcstel da\u011f\u0131l\u0131m, sabit bir ortalama h\u0131zla ba\u011f\u0131ms\u0131z bi\u00e7imde ger\u00e7ekle\u015fen ard\u0131\u015f\u0131k olaylar aras\u0131ndaki s\u00fcreyi modeller. Tek parametresi \\(\\lambda\\) her \u015feyi belirler; ortalama bekleme s\u00fcresi tam olarak \\(1\/\\lambda\\) kadard\u0131r.<\/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>\u00dcstel Da\u011f\u0131l\u0131m \u2013 Hesaplama \u00d6rne\u011fi<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> bir \u00e7a\u011fr\u0131 merkezine saatte ortalama 2 \u00e7a\u011fr\u0131 geliyor. Bir sonraki \u00e7a\u011fr\u0131n\u0131n 1 saat i\u00e7inde gelme olas\u0131l\u0131\u011f\u0131 nedir ve 1 ile 2 saat aras\u0131nda gelme \u015fans\u0131 nedir?<\/p>\n<p>\\[ \\lambda t = 2 \\times 1 = 2 \\]<\/p>\n<p>\\[ F(1) = 1 - e^{-2} = 1 - 0.1353 = 0.8647 \\]<\/p>\n<p>\\[ P(1 \\le X \\le 2) = e^{-2} - e^{-4} = 0.1353 - 0.0183 = 0.1170 \\]<\/p>\n<p><strong>Sonu\u00e7:<\/strong> P(X \u2264 1 saat) = %86,47, P(X &gt; 1 saat) = %13,53 ve P(1 saat \u2264 X \u2264 2 saat) = %11,70. t = 1 saat an\u0131ndaki yo\u011funluk f(1) = 2e\u207b\u00b2 \u2248 saat ba\u015f\u0131na 0,2707, ortalama bekleme s\u00fcresi 0,5 saat (30 dakika), medyan ise ln(2)\/2 \u2248 0,3466 saat (~20,8 dakika). Bunlar, hesaplay\u0131c\u0131n\u0131n varsay\u0131lan ayarlar\u0131yla g\u00f6sterdi\u011fi de\u011ferlerin ayn\u0131s\u0131d\u0131r.<\/p>\n<p>\n\r\n<\/section>\n<h2>Hesaplay\u0131c\u0131 Nas\u0131l Kullan\u0131l\u0131r?<\/h2>\n<ol>\n<li><strong>Parametreyi belirtme y\u00f6ntemi<\/strong> men\u00fcs\u00fcn\u00fc a\u00e7\u0131n ve oran \\(\\lambda\\) (zaman ba\u015f\u0131na olay say\u0131s\u0131) m\u0131 yoksa ortalama bekleme s\u00fcresi \\(\\mu\\) m\u00fc girmek istedi\u011finizi se\u00e7in. Yaln\u0131zca ilgili alan g\u00f6sterilir.<\/li>\n<li>Oran\u0131 se\u00e7tiyseniz <strong>Oran (\u03bb)<\/strong> alan\u0131n\u0131 doldurun ve hangi zaman birimiyle ifade edildi\u011fini se\u00e7in (saniye ba\u015f\u0131na, dakika ba\u015f\u0131na, saat ba\u015f\u0131na, g\u00fcn ba\u015f\u0131na, y\u0131l ba\u015f\u0131na). Ortalamay\u0131 se\u00e7tiyseniz bunun yerine <strong>Ortalama bekleme s\u00fcresi (\u03bc)<\/strong> alan\u0131n\u0131 birimiyle birlikte doldurun; hesaplay\u0131c\u0131 bunu \\(\\lambda = 1\/\\mu\\) \u00fczerinden d\u00f6n\u00fc\u015ft\u00fcr\u00fcr.<\/li>\n<li><strong>S\u00fcre (t)<\/strong> alan\u0131na ilgilenilen bekleme s\u00fcresini girin ve alt\u0131ndaki \"birim\" se\u00e7ene\u011finden birimini se\u00e7in.<\/li>\n<li>\u0130ste\u011fe ba\u011fl\u0131 olarak <strong>Aral\u0131k sonu (b)<\/strong> alan\u0131n\u0131 doldurarak \\(P(t \\le X \\le b)\\) olas\u0131l\u0131\u011f\u0131n\u0131 da hesaplatabilirsiniz. Bu sonucu istemiyorsan\u0131z bo\u015f b\u0131rak\u0131n.<\/li>\n<li>Sonu\u00e7lar\u0131 okuyun: yo\u011funluk \\(f(t)\\), k\u00fcm\u00fclatif olas\u0131l\u0131k \\(P(X \\le t)\\), sa\u011fkal\u0131m olas\u0131l\u0131\u011f\u0131 \\(P(X &gt; t)\\), aral\u0131k olas\u0131l\u0131\u011f\u0131, ortalama bekleme s\u00fcresi ve medyan ile 90. y\u00fczdelik bekleme s\u00fcresi ile sade dille bir yorum i\u00e7eren \u00f6zet sat\u0131r\u0131.<\/li>\n<\/ol>\n<h2>\u00dcstel Da\u011f\u0131l\u0131m Nedir?<\/h2>\n<p>\u00dcstel da\u011f\u0131l\u0131m, olaylar\u0131n ba\u011f\u0131ms\u0131z olarak sabit bir ortalama h\u0131zla ger\u00e7ekle\u015fti\u011fi bir s\u00fcre\u00e7te \u2014 bir <em>Poisson s\u00fcrecinde<\/em> \u2014 bir sonraki olaya kadar ge\u00e7en bekleme s\u00fcresini tan\u0131mlar. Tipik uygulama alanlar\u0131 aras\u0131nda m\u00fc\u015fteri var\u0131\u015flar\u0131 aras\u0131ndaki s\u00fcre, radyoaktif bir par\u00e7ac\u0131\u011f\u0131n bozunmas\u0131na kadar ge\u00e7en s\u00fcre, elektronik bir bile\u015fenin \u00f6mr\u00fc veya bir sunucunun bir sonraki ar\u0131zas\u0131na kadar ge\u00e7en s\u00fcre yer al\u0131r.<\/p>\n<p>Da\u011f\u0131l\u0131m tek bir parametreyle, oran \\(\\lambda\\) ile tan\u0131mlan\u0131r. Olas\u0131l\u0131k yo\u011funlu\u011fu \\(f(t) = \\lambda e^{-\\lambda t}\\) \\(t = 0\\) an\u0131nda en b\u00fcy\u00fckt\u00fcr ve p\u00fcr\u00fczs\u00fczce azal\u0131r; bu da k\u0131sa beklemelerin en olas\u0131 oldu\u011fu anlam\u0131na gelir. K\u00fcm\u00fclatif fonksiyon \\(F(t) = 1 - e^{-\\lambda t}\\), bekle\u015fin \\(t\\) an\u0131nda ya da \u00f6ncesinde sona erme olas\u0131l\u0131\u011f\u0131n\u0131 verir; t\u00fcmleyeni olan sa\u011fkal\u0131m fonksiyonu \\(S(t) = e^{-\\lambda t}\\) ise \\(t\\)'den sonra h\u00e2l\u00e2 bekliyor olma olas\u0131l\u0131\u011f\u0131n\u0131 verir.<\/p>\n<p>Ortalama ve standart sapma ikisi de \\(1\/\\lambda\\)'d\u0131r, ancak medyan \\(\\ln(2)\/\\lambda \\approx 0.693\/\\lambda\\) daha k\u00fc\u00e7\u00fckt\u00fcr. Bu size pratik bir bilgi verir: beklemelerin yar\u0131s\u0131ndan fazlas\u0131 ortalama s\u00fcreden \u00f6nce sona erer. \u00c7ok uzun bir bekleme m\u00fcmk\u00fcnd\u00fcr ama giderek daha nadir h\u00e2le gelir \u2014 \u00f6rne\u011fin beklemelerin yaln\u0131zca %5'i \\(3\/\\lambda\\) de\u011ferini a\u015far.<\/p>\n<p>\u00dcstel da\u011f\u0131l\u0131m\u0131n belirleyici \u00f6zelli\u011fi <strong>haf\u0131zas\u0131zl\u0131k<\/strong>t\u0131r: \\(P(X &gt; s + t \\mid X &gt; s) = P(X &gt; t)\\). Bir ampul\u00fcn \u00f6mr\u00fc \u00fcstel da\u011f\u0131l\u0131ml\u0131ysa ve bir y\u0131ld\u0131r yan\u0131yorsa, bir y\u0131l daha dayanma \u015fans\u0131 yeniykenkiyle tamamen ayn\u0131d\u0131r. Bu \u00f6zellik da\u011f\u0131l\u0131m\u0131 geometrik da\u011f\u0131l\u0131m\u0131n s\u00fcrekli kar\u015f\u0131l\u0131\u011f\u0131 yapar ve olaylar aras\u0131ndaki s\u00fcre yerine sabit bir d\u00f6nemdeki olay <em>say\u0131s\u0131n\u0131<\/em> tan\u0131mlayan <a href=\"https:\/\/wpcalc.com\/tr\/istatistik\/poisson-dagilimi-hesaplama\/\">Poisson da\u011f\u0131l\u0131m\u0131n\u0131n<\/a> do\u011fal yol arkada\u015f\u0131 h\u00e2line getirir.<\/p>\n<h2>Varsay\u0131mlar, S\u0131n\u0131rlamalar ve \u0130pu\u00e7lar\u0131<\/h2>\n<ul>\n<li><strong>Sabit oran.<\/strong> Model, olaylar\u0131n her zaman sabit bir ortalama h\u0131zla ger\u00e7ekle\u015fti\u011fini varsayar. Oran de\u011fi\u015firse (\u00f6r. yo\u011fun saat var\u0131\u015flar\u0131, mekanik par\u00e7alar\u0131n y\u0131pranmas\u0131) \u00fcstel da\u011f\u0131l\u0131m olas\u0131l\u0131klar\u0131 oldu\u011fundan d\u00fc\u015f\u00fck ya da y\u00fcksek tahmin eder.<\/li>\n<li><strong>Ba\u011f\u0131ms\u0131zl\u0131k.<\/strong> Bir olay, bir sonraki olay\u0131n zaman\u0131n\u0131 etkilememelidir. Olaylar\u0131n k\u00fcmele\u015fmesi bu varsay\u0131m\u0131 ihlal eder.<\/li>\n<li><strong>Haf\u0131zas\u0131zl\u0131k.<\/strong> S\u00fcre\u00e7 ger\u00e7ekten \u00fcstelse, ge\u00e7mi\u015f bekleme s\u00fcresi kalan bekleme hakk\u0131nda hi\u00e7bir bilgi ta\u015f\u0131maz. Makinelerin ve insanlar\u0131n ger\u00e7ek \u00f6m\u00fcrleri genellikle haf\u0131zas\u0131z de\u011fildir; bunlar i\u00e7in Weibull da\u011f\u0131l\u0131m\u0131 gibi g\u00fcvenilirlik modelleri daha iyi uyar.<\/li>\n<li><strong>Birimler.<\/strong> Hesaplay\u0131c\u0131 t\u00fcm birimleri dahili olarak d\u00f6n\u00fc\u015ft\u00fcr\u00fcr; bu y\u00fczden oran\u0131 saat ba\u015f\u0131na, s\u00fcreyi dakika cinsinden, hi\u00e7bir aritmetik yapmadan girebilirsiniz. Bir y\u0131l 365 g\u00fcn olarak al\u0131n\u0131r.<\/li>\n<li><strong>Yo\u011funluk ile olas\u0131l\u0131k.<\/strong> \\(f(t)\\) birim zaman ba\u015f\u0131na bir yo\u011funluktur, olas\u0131l\u0131k de\u011fildir \u2014 1'i a\u015fabilir. Anlaml\u0131 olas\u0131l\u0131k ifadeleri \\(F(t)\\), \\(S(t)\\) ve aral\u0131k olas\u0131l\u0131\u011f\u0131d\u0131r.<\/li>\n<li>Bekleme s\u00fcreleri yerine olay say\u0131lar\u0131n\u0131 modellemeniz gerekiyorsa <a href=\"https:\/\/wpcalc.com\/tr\/istatistik\/poisson-dagilimi-hesaplama\/\">Poisson da\u011f\u0131l\u0131m\u0131 hesaplay\u0131c\u0131s\u0131n\u0131<\/a> kullan\u0131n; sabit say\u0131da denemedeki evet\/hay\u0131r sonu\u00e7lar\u0131 i\u00e7in <a href=\"https:\/\/wpcalc.com\/tr\/istatistik\/binom-dagilimi-hesaplama\/\">binom da\u011f\u0131l\u0131m\u0131 hesaplay\u0131c\u0131s\u0131na<\/a>, simetrik s\u00fcrekli veriler i\u00e7in ise <a href=\"https:\/\/wpcalc.com\/tr\/istatistik\/normal-dagilim-hesaplayici\/\">normal da\u011f\u0131l\u0131m hesaplay\u0131c\u0131s\u0131na<\/a> bak\u0131n.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Oran \u03bb veya ortalama bekleme s\u00fcresiyle \u00fcstel da\u011f\u0131l\u0131m olas\u0131l\u0131klar\u0131n\u0131 hesaplay\u0131n: yo\u011funluk, P(X \u2264 t), P(X > t), aral\u0131k olas\u0131l\u0131\u011f\u0131, ortalama ve medyan. Oran\u0131, bir s\u00fcreyi ve iste\u011fe ba\u011fl\u0131 bir aral\u0131k sonunu 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-359","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\/359","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=359"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/359\/revisions"}],"predecessor-version":[{"id":3770,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/359\/revisions\/3770"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=359"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=359"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=359"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}