{"id":110,"date":"2023-08-05T09:10:02","date_gmt":"2023-08-05T09:10:02","guid":{"rendered":"https:\/\/statorials.org\/tr\/dagitim-islevi\/"},"modified":"2023-08-05T09:10:02","modified_gmt":"2023-08-05T09:10:02","slug":"dagitim-islevi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/dagitim-islevi\/","title":{"rendered":"Da\u011f\u0131t\u0131m i\u015flevi"},"content":{"rendered":"<p>Bu yaz\u0131da da\u011f\u0131t\u0131m fonksiyonunun a\u00e7\u0131klamas\u0131n\u0131, de\u011ferlerinin nas\u0131l hesapland\u0131\u011f\u0131n\u0131 ve da\u011f\u0131t\u0131m fonksiyonunun ger\u00e7ek d\u00fcnyadan bir \u00f6rne\u011fini bulacaks\u0131n\u0131z. Ayr\u0131ca da\u011f\u0131l\u0131m fonksiyonu ile yo\u011funluk fonksiyonu aras\u0131ndaki farklar\u0131 da g\u00f6rebileceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-funcion-de-distribucion\"><\/span> Da\u011f\u0131t\u0131m fonksiyonu nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>K\u00fcm\u00fclatif da\u011f\u0131l\u0131m<\/strong> <strong>fonksiyonu olarak da adland\u0131r\u0131lan da\u011f\u0131l\u0131m fonksiyonu<\/strong> , bir da\u011f\u0131l\u0131m\u0131n k\u00fcm\u00fclatif olas\u0131l\u0131\u011f\u0131n\u0131 g\u00f6steren matematiksel bir fonksiyondur. Yani herhangi bir de\u011fere ait da\u011f\u0131l\u0131m fonksiyonunun g\u00f6r\u00fcnt\u00fcs\u00fc, de\u011fi\u015fkenin o de\u011feri veya daha d\u00fc\u015f\u00fck bir de\u011feri alma olas\u0131l\u0131\u011f\u0131na e\u015fittir.<\/p>\n<p> K\u00fcm\u00fclatif da\u011f\u0131t\u0131m fonksiyonu, genel sembol\u00fc b\u00fcy\u00fck F olmas\u0131na ra\u011fmen FDA k\u0131saltmas\u0131yla da an\u0131labilir.<\/p>\n<p> Bu nedenle da\u011f\u0131t\u0131m fonksiyonu a\u015fa\u011f\u0131daki form\u00fclle tan\u0131mlan\u0131r: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c8cf5efd36881f74974a11b10af2dd4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"F(x)=P[X\\leq x]\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-la-funcion-de-distribucion\"><\/span> Da\u011f\u0131t\u0131m fonksiyonu nas\u0131l hesaplan\u0131r<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Daha sonra olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n kesikli veya s\u00fcrekli olmas\u0131na ba\u011fl\u0131 olarak da\u011f\u0131l\u0131m fonksiyonunun de\u011ferinin nas\u0131l hesaplanaca\u011f\u0131n\u0131 a\u00e7\u0131kl\u0131yoruz.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caso-discreto\"><\/span> Gizli kutu<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Rastgele de\u011fi\u015fken ayr\u0131k ise, k\u00fcm\u00fclatif da\u011f\u0131l\u0131m fonksiyonu <em>x&#8217;e<\/em> e\u015fit veya ondan k\u00fc\u00e7\u00fck t\u00fcm de\u011ferlerin olas\u0131l\u0131klar\u0131n\u0131n toplam\u0131na e\u015fittir.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c3b978075c7791d3379a8c170010eb2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle F(x)=P[X\\leq x]=\\sum_{u\\leq x}f(u)\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"222\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p> Alt\u0131n<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5875573ff1b51b9b17fc81a368fabc07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(u)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p> ayr\u0131k de\u011fi\u015fkenle ili\u015fkili olas\u0131l\u0131k fonksiyonudur.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caso-continuo\"><\/span> Devam eden dava<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Rastgele de\u011fi\u015fken s\u00fcrekli ise, k\u00fcm\u00fclatif da\u011f\u0131l\u0131m fonksiyonu yo\u011funluk fonksiyonunun eksi sonsuzdan s\u00f6z konusu de\u011fere kadar olan integraline e\u015fde\u011ferdir.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-36434a36d91add71ad209868965d6ccb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle F(x)=P[X\\leq x]=\\int_{-\\infty}^{x}f(u)du\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"250\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Alt\u0131n<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5875573ff1b51b9b17fc81a368fabc07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(u)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p> s\u00fcrekli de\u011fi\u015fkenle ili\u015fkili yo\u011funluk fonksiyonudur. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-funcion-de-distribucion\"><\/span> Da\u011f\u0131t\u0131m Fonksiyonu \u00d6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Art\u0131k da\u011f\u0131t\u0131m fonksiyonunun tan\u0131m\u0131n\u0131 bildi\u011fimize g\u00f6re, bir da\u011f\u0131t\u0131m fonksiyonu de\u011ferinin nas\u0131l hesaplanaca\u011f\u0131n\u0131 \u00f6\u011frenmek i\u00e7in ad\u0131m ad\u0131m pratik bir \u00f6rne\u011fe bakal\u0131m.<\/p>\n<ul>\n<li> Bir madeni paran\u0131n d\u00f6rt kez at\u0131lmas\u0131yla ilgili rastgele deney i\u00e7in da\u011f\u0131l\u0131m fonksiyonunu hesaplay\u0131n.<\/li>\n<\/ul>\n<p> Al\u0131\u015ft\u0131rmay\u0131 \u00e7\u00f6zmek i\u00e7in \u00f6ncelikle d\u00f6rt yaz\u0131-tura at\u0131\u015f\u0131 s\u0131ras\u0131nda elde edilen tura say\u0131s\u0131yla ilgili t\u00fcm olas\u0131l\u0131klar\u0131 hesaplaman\u0131z gerekir: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/probabilite-lancer-quatre-pieces.png\" alt=\"d\u00f6rt madeni paray\u0131 havaya atma olas\u0131l\u0131\u011f\u0131\" class=\"wp-image-2346\" width=\"492\" height=\"331\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Dolay\u0131s\u0131yla kesikli bir de\u011fi\u015fken oldu\u011fundan da\u011f\u0131l\u0131m fonksiyonunun g\u00f6r\u00fcnt\u00fclerini belirlemek i\u00e7in s\u00f6z konusu de\u011fi\u015fkenin de\u011ferine kadar olas\u0131l\u0131klar\u0131 toplamak yeterlidir:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-63c3574be5cdcf6de8b54f910c01e35e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}F(X\\leq 0)=f(0)=0,0625\\\\[4ex]\\begin{aligned}F(X\\leq 1)&amp; =f(0)+f(1)\\\\[1.1ex] &amp; =0,0625+0,25=0,3125\\end{aligned}\\\\[6ex]\\begin{aligned}F(X\\leq 2)&amp; =f(0)+f(1)+f(2)\\\\[1.1ex] &amp; =0,0625+0,25+0,375=0,6875\\end{aligned}\\\\[6ex]\\begin{aligned}F(X\\leq 3)&amp; =f(0)+f(1)+f(2)+f(3)\\\\[1.1ex] &amp; =0,0625+0,25+0,375+0,25=0,9375\\end{aligned}\\\\[6ex]\\begin{aligned}F(X\\leq 4)&amp; =f(0)+f(1)+f(2)+f(3)+f(4)\\\\[1.1ex] &amp; =0,0625+0,25+0,375+0,25+0,0625=1\\end{aligned}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"363\" width=\"435\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> B\u00f6ylece d\u00f6rt ba\u011f\u0131ms\u0131z paran\u0131n at\u0131lmas\u0131yla tura at\u0131lmas\u0131n\u0131n da\u011f\u0131l\u0131m fonksiyonunun de\u011ferleri a\u015fa\u011f\u0131daki gibidir: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/probabilite-cumulative-lancer-quatre-pieces.png\" alt=\"\" class=\"wp-image-2362\" width=\"224\" height=\"331\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-la-funcion-de-distribucion\"><\/span> Da\u011f\u0131t\u0131m fonksiyonunun \u00f6zellikleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> De\u011fi\u015fkenin t\u00fcr\u00fcnden ba\u011f\u0131ms\u0131z olarak da\u011f\u0131t\u0131m fonksiyonu her zaman a\u015fa\u011f\u0131daki \u00f6zelliklere sahiptir:<\/p>\n<ul>\n<li> K\u00fcm\u00fclatif da\u011f\u0131l\u0131m fonksiyonunun de\u011feri 0 ile 1 dahil aras\u0131ndad\u0131r.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-b43459e3f1bfcf6f783408bb57f2b823_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0\\leq F(x) \\leq 1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"102\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> <em>X<\/em> sonsuza giderken bir da\u011f\u0131l\u0131m fonksiyonunun limiti 1&#8217;e e\u015fittir.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-18a8b8bd2a28b6e5bf66af92771f690e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty} F(x)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"118\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<ul>\n<li> \u00d6te yandan, <em>x<\/em> eksi sonsuza yakla\u015f\u0131rken bir da\u011f\u0131l\u0131m fonksiyonunun limiti s\u0131f\u0131rd\u0131r.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-121e332e607371288d172844a59d5e8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to -\\infty} F(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"119\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> \u00d6zellikleri gere\u011fi da\u011f\u0131l\u0131m fonksiyonu monotondur ve azalmaz.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1b3f9780a83c58a6add1513c112f601b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_1 \\leq x_2 \\implies F(x_1)\\leq F(x_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"221\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Ayr\u0131ca, e\u011fer\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-42ce2269b42ed638b79b5c3e01e8d34c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\\leq b\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"41\" style=\"vertical-align: -3px;\"><\/p>\n<p> a\u015fa\u011f\u0131daki denklemler sa\u011flan\u0131r. <\/li>\n<\/ul>\n<pre class=\"ql-errors\"> *** QuickLaTeX cannot compile formula:\n\\begin{array}{l}P(X &lt; a) = F(a^-)\\\\[2ex] P(X&gt;a)=1-F(a)\\\\[2ex]P(X \\ge a )=1-F(a^-)\\\\[2ex]P(a&lt;ul&gt;&lt;li&gt; Finally, if the statistical variable is continuous, the following equality is satisfied: &lt;\/li&gt;&lt;\/ul&gt;[latex ]\\begin{array}{l}P(a \\le X &lt; b) = \\displaystyle\\int_{a}^{b}f(x)\\,dx = F(b)- F(a)\\end{array}\n\n*** Error message:\nMissing $ inserted.\nleading text: \\begin{array}{l}\nPlease use \\mathaccent for accents in math mode.\nleading text: ... the statistical variable is continuous, the\nPlease use \\mathaccent for accents in math mode.\nleading text: ...iable statistic is continuous, equality\n\\begin{array} on input line 8 ended by \\end{document}.\nleading text: \\end{document}\nImproper \\prevdepth.\nleading text: \\end{document}\nMissing $ inserted.\nleading text: \\end{document}\nMissing } inserted.\nleading text: \\end{document}\nMissing \\cr inserted.\nleading text: \\end{document}\nMissing $ inserted.\nleading text: \\end{document}\nYou can't use `\\end' in internal vertical mode.\nleading text: \\end{document}\n\\begin{array} on input line 8 ended by \\end{document}.\nleading text: \\end{document}\n\n<\/pre>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"funcion-de-distribucion-y-funcion-de-densidad\"><\/span> Da\u011f\u0131t\u0131m fonksiyonu ve yo\u011funluk fonksiyonu<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Son olarak, bu iki istatistiksel kavram s\u0131kl\u0131kla kar\u0131\u015ft\u0131r\u0131ld\u0131\u011f\u0131 i\u00e7in da\u011f\u0131l\u0131m fonksiyonu ile yo\u011funluk fonksiyonu aras\u0131ndaki fark\u0131n ne oldu\u011funu g\u00f6rece\u011fiz.<\/p>\n<p> <strong>Da\u011f\u0131l\u0131m fonksiyonu ile yo\u011funluk fonksiyonu aras\u0131ndaki fark,<\/strong> tan\u0131mlad\u0131klar\u0131 olas\u0131l\u0131k t\u00fcr\u00fcd\u00fcr. Yo\u011funluk fonksiyonu de\u011fi\u015fkenin belirli bir de\u011fer alma olas\u0131l\u0131\u011f\u0131n\u0131, da\u011f\u0131l\u0131m fonksiyonu ise de\u011fi\u015fkenin k\u00fcm\u00fclatif olas\u0131l\u0131\u011f\u0131n\u0131 a\u00e7\u0131klar.<\/p>\n<p> Yani de\u011fi\u015fkenin belirli bir de\u011fere e\u015fit veya daha k\u00fc\u00e7\u00fck olma olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in da\u011f\u0131l\u0131m fonksiyonu kullan\u0131l\u0131r.<\/p>\n<p> Yo\u011funluk fonksiyonunun yaln\u0131zca s\u00fcrekli de\u011fi\u015fkenlere at\u0131fta bulundu\u011funu, dolay\u0131s\u0131yla bu ayr\u0131m\u0131n yaln\u0131zca \u00fczerinde \u00e7al\u0131\u015f\u0131lan de\u011fi\u015fkenin s\u00fcrekli olmas\u0131 durumunda anlaml\u0131 oldu\u011funu unutmay\u0131n.<\/p>\n<p> Ortalamas\u0131 1 ve standart sapmas\u0131 0,5 olan normal bir da\u011f\u0131l\u0131m izleyen bir de\u011fi\u015fkenin yo\u011funluk fonksiyonuyla kar\u015f\u0131la\u015ft\u0131r\u0131ld\u0131\u011f\u0131nda da\u011f\u0131l\u0131m fonksiyonunun grafiksel g\u00f6steriminin nas\u0131l de\u011fi\u015fti\u011fine dikkat edin: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/fonction-de-distribution-et-fonction-de-densite.png\" alt=\"da\u011f\u0131t\u0131m fonksiyonu ile yo\u011funluk fonksiyonu aras\u0131ndaki fark\" class=\"wp-image-2375\" width=\"478\" height=\"297\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Yo\u011funluk i\u015flevi hakk\u0131nda daha fazla bilgi edinmek i\u00e7in a\u015fa\u011f\u0131daki makaleye bak\u0131n: <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/yogunluk-fonksiyonu\/\">yo\u011funluk fonksiyonu<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu yaz\u0131da da\u011f\u0131t\u0131m fonksiyonunun a\u00e7\u0131klamas\u0131n\u0131, de\u011ferlerinin nas\u0131l hesapland\u0131\u011f\u0131n\u0131 ve da\u011f\u0131t\u0131m fonksiyonunun ger\u00e7ek d\u00fcnyadan bir \u00f6rne\u011fini bulacaks\u0131n\u0131z. Ayr\u0131ca da\u011f\u0131l\u0131m fonksiyonu ile yo\u011funluk fonksiyonu aras\u0131ndaki farklar\u0131 da g\u00f6rebileceksiniz. Da\u011f\u0131t\u0131m fonksiyonu nedir? K\u00fcm\u00fclatif da\u011f\u0131l\u0131m fonksiyonu olarak da adland\u0131r\u0131lan da\u011f\u0131l\u0131m fonksiyonu , bir da\u011f\u0131l\u0131m\u0131n k\u00fcm\u00fclatif olas\u0131l\u0131\u011f\u0131n\u0131 g\u00f6steren matematiksel bir fonksiyondur. Yani herhangi bir de\u011fere ait da\u011f\u0131l\u0131m fonksiyonunun g\u00f6r\u00fcnt\u00fcs\u00fc, de\u011fi\u015fkenin [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-110","post","type-post","status-publish","format-standard","hentry","category-olasilik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Da\u011f\u0131t\u0131m fonksiyonu: nedir, hesaplama, \u00f6rnek, \u00f6zellikler...<\/title>\n<meta name=\"description\" content=\"Burada bir da\u011f\u0131t\u0131m fonksiyonunun ne oldu\u011funu, de\u011ferlerinin nas\u0131l hesapland\u0131\u011f\u0131n\u0131 ve da\u011f\u0131t\u0131m fonksiyonunun ger\u00e7ek d\u00fcnyadan bir \u00f6rne\u011fini bulacaks\u0131n\u0131z.\" \/>\n<meta name=\"robots\" content=\"index, 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