{"id":113,"date":"2023-08-05T08:29:06","date_gmt":"2023-08-05T08:29:06","guid":{"rendered":"https:\/\/statorials.org\/tr\/yogunluk-fonksiyonu\/"},"modified":"2023-08-05T08:29:06","modified_gmt":"2023-08-05T08:29:06","slug":"yogunluk-fonksiyonu","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/yogunluk-fonksiyonu\/","title":{"rendered":"Yo\u011funluk fonksiyonu"},"content":{"rendered":"<p>Bu makalede yo\u011funluk fonksiyonunun ne oldu\u011funu, yo\u011funluk fonksiyonundan olas\u0131l\u0131\u011f\u0131n nas\u0131l hesapland\u0131\u011f\u0131n\u0131 ve bu olas\u0131l\u0131k fonksiyonunun \u00f6zelliklerini ke\u015ffedeceksiniz. Ek olarak yo\u011funluk fonksiyonu ile da\u011f\u0131l\u0131m fonksiyonu aras\u0131ndaki farklar\u0131n ne oldu\u011funu g\u00f6rebileceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-funcion-de-densidad\"><\/span> Yo\u011funluk fonksiyonu nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Olas\u0131l\u0131k yo\u011funluk<\/strong> <strong>fonksiyonu olarak da adland\u0131r\u0131lan yo\u011funluk fonksiyonu<\/strong> , s\u00fcrekli bir rastgele de\u011fi\u015fkenin belirli bir de\u011feri alma olas\u0131l\u0131\u011f\u0131n\u0131 a\u00e7\u0131klayan matematiksel bir fonksiyondur.<\/p>\n<p> Ba\u015fka bir deyi\u015fle, bir de\u011fi\u015fkene ili\u015fkin yo\u011funluk fonksiyonu, de\u011fi\u015fkenin de\u011fer alma olas\u0131l\u0131klar\u0131n\u0131 matematiksel olarak tan\u0131mlar.<\/p>\n<p> \u00d6rne\u011fin, bir pop\u00fclasyonda yeti\u015fkin bir ki\u015finin 1,80 m&#8217;den uzun olma olas\u0131l\u0131\u011f\u0131 %35 olsun, bu durumda yo\u011funluk fonksiyonu s\u00f6z konusu olas\u0131l\u0131\u011f\u0131 hesaplarken %35&#8217;lik bir olas\u0131l\u0131\u011f\u0131 g\u00f6sterecektir.<\/p>\n<p> Bazen olas\u0131l\u0131k yo\u011funluk fonksiyonu PDF olarak k\u0131salt\u0131l\u0131r. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calcular-una-probabilidad-con-la-funcion-de-densidad\"><\/span> Yo\u011funluk fonksiyonuyla olas\u0131l\u0131k hesaplama<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> S\u00fcrekli bir de\u011fi\u015fkenin bir aral\u0131kta de\u011fer alma olas\u0131l\u0131\u011f\u0131n\u0131 bulmak i\u00e7in, s\u00f6z konusu de\u011fi\u015fkene ili\u015fkin yo\u011funluk fonksiyonunun aral\u0131\u011f\u0131n s\u0131n\u0131rlar\u0131 aras\u0131ndaki integralinin hesaplanmas\u0131 gerekir.<\/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-92039c09fd43ec161f625ab7a08daf44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[a\\leq X\\leq b]=\\int_a^b f(x)dx\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"209\" 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-f9cec16914b323374b5501f2f4c2719a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p> s\u00fcrekli rastgele de\u011fi\u015fkenin yo\u011funluk fonksiyonudur.<\/p>\n<p> Veya di\u011fer bir deyi\u015fle de\u011fi\u015fkenin bir aral\u0131kta de\u011fer alma olas\u0131l\u0131\u011f\u0131, o aral\u0131kta yo\u011funluk fonksiyonunun alt\u0131nda kalan alana e\u015fittir. <\/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-densite.png\" alt=\"Yo\u011funluk fonksiyonu\" class=\"wp-image-2429\" width=\"267\" height=\"266\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Olas\u0131l\u0131k hesaplamas\u0131n\u0131n ancak istatistiksel de\u011fi\u015fkenin normal da\u011f\u0131l\u0131m, \u00fcstel da\u011f\u0131l\u0131m, Poisson da\u011f\u0131l\u0131m\u0131 vb. gibi s\u00fcrekli bir da\u011f\u0131l\u0131m izlemesi durumunda bu \u015fekilde yap\u0131labilece\u011fini unutmay\u0131n. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-la-funcion-de-densidad\"><\/span> Yo\u011funluk fonksiyonunun \u00f6zellikleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Yo\u011funluk fonksiyonu a\u015fa\u011f\u0131daki \u00f6zelliklere sahiptir:<\/p>\n<ul>\n<li> Yo\u011funluk fonksiyonunun de\u011feri herhangi bir x de\u011feri i\u00e7in s\u0131f\u0131r veya pozitiftir.<\/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-9ef1721c5f1a67b3b64b3b625286ea23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\\geq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"67\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Ayr\u0131ca yo\u011funluk fonksiyonunun maksimum de\u011feri 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-acfd4f51cf2602bac813da61fa5429ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\\leq 1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Asl\u0131nda yo\u011funluk fonksiyonu grafi\u011finin alt\u0131ndaki toplam alan, t\u00fcm olas\u0131l\u0131klar k\u00fcmesine kar\u015f\u0131l\u0131k geldi\u011finden, de\u011fi\u015fken ne olursa olsun her zaman 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-25d2e58d1bcce79e3baff26b6017019c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\int_{-\\infty}^{+\\infty} f(x)dx=1\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"131\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<ul>\n<li> \u00d6nceki b\u00f6l\u00fcmde a\u00e7\u0131kland\u0131\u011f\u0131 gibi s\u00fcrekli bir de\u011fi\u015fkenin bir aral\u0131kta de\u011fer alma olas\u0131l\u0131\u011f\u0131, yo\u011funluk fonksiyonunun o aral\u0131ktaki integrali ile hesaplan\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-0d27660508b38e9e436218365f9d8333_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[a\\leq X\\leq b]=\\int_a^b f(x)dx=F(b)-F(a)\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"325\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"funcion-de-densidad-y-funcion-de-distribucion\"><\/span> Yo\u011funluk fonksiyonu ve da\u011f\u0131t\u0131m fonksiyonu<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bu son b\u00f6l\u00fcmde yo\u011funluk fonksiyonu ile da\u011f\u0131l\u0131m fonksiyonunun ne kadar farkl\u0131 oldu\u011funu g\u00f6rece\u011fiz \u00e7\u00fcnk\u00fc bunlar genellikle kar\u0131\u015ft\u0131r\u0131lan iki t\u00fcr olas\u0131l\u0131ksal fonksiyondur.<\/p>\n<p> Matematiksel olarak <strong>da\u011f\u0131l\u0131m fonksiyonu yo\u011funluk fonksiyonunun integraline e\u015fde\u011ferdir<\/strong> , dolay\u0131s\u0131yla da\u011f\u0131l\u0131m fonksiyonu s\u00fcrekli bir de\u011fi\u015fkenin k\u00fcm\u00fclatif olas\u0131l\u0131\u011f\u0131n\u0131 tan\u0131mlar.<\/p>\n<p> 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> Dolay\u0131s\u0131yla bu iki fonksiyon t\u00fcr\u00fc aras\u0131ndaki matematiksel ili\u015fki a\u015fa\u011f\u0131daki gibidir:<\/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-ed8d06734f95b294b944fd890d648d79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq a]=\\int_{-\\infty}^a f(x)dx=F(a)\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"248\" 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-f9cec16914b323374b5501f2f4c2719a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p> yo\u011funluk fonksiyonudur ve<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-24256e5abe32d819f1d96f3e9df91bb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"F(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\"><\/p>\n<p> da\u011f\u0131t\u0131m fonksiyonudur.<\/p>\n<p> Yo\u011funluk fonksiyonunun grafiksel g\u00f6steriminin, ortalamas\u0131 1 ve standart sapmas\u0131 0,5 olan normal bir da\u011f\u0131l\u0131m izleyen bir de\u011fi\u015fkenin da\u011f\u0131l\u0131m fonksiyonuna g\u00f6re 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> Da\u011f\u0131t\u0131m \u00f6zelli\u011fi hakk\u0131nda daha fazla bilgi edinmek i\u00e7in a\u015fa\u011f\u0131daki ba\u011flant\u0131ya t\u0131klay\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\/dagitim-islevi\/\">da\u011f\u0131t\u0131m fonksiyonu<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede yo\u011funluk fonksiyonunun ne oldu\u011funu, yo\u011funluk fonksiyonundan olas\u0131l\u0131\u011f\u0131n nas\u0131l hesapland\u0131\u011f\u0131n\u0131 ve bu olas\u0131l\u0131k fonksiyonunun \u00f6zelliklerini ke\u015ffedeceksiniz. Ek olarak yo\u011funluk fonksiyonu ile da\u011f\u0131l\u0131m fonksiyonu aras\u0131ndaki farklar\u0131n ne oldu\u011funu g\u00f6rebileceksiniz. Yo\u011funluk fonksiyonu nedir? Olas\u0131l\u0131k yo\u011funluk fonksiyonu olarak da adland\u0131r\u0131lan yo\u011funluk fonksiyonu , s\u00fcrekli bir rastgele de\u011fi\u015fkenin belirli bir de\u011feri alma olas\u0131l\u0131\u011f\u0131n\u0131 a\u00e7\u0131klayan matematiksel bir fonksiyondur. Ba\u015fka [&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-113","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>\u25b7 Yo\u011funluk fonksiyonu nedir? 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