{"id":118,"date":"2023-08-05T07:09:34","date_gmt":"2023-08-05T07:09:34","guid":{"rendered":"https:\/\/statorials.org\/tr\/olasilik-fonksiyonu\/"},"modified":"2023-08-05T07:09:34","modified_gmt":"2023-08-05T07:09:34","slug":"olasilik-fonksiyonu","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/olasilik-fonksiyonu\/","title":{"rendered":"Olas\u0131l\u0131k fonksiyonu"},"content":{"rendered":"<p>Bu makalede olas\u0131l\u0131k fonksiyonlar\u0131n\u0131n ne oldu\u011fu a\u00e7\u0131klanmaktad\u0131r. B\u00f6ylece olas\u0131l\u0131k fonksiyonunun anlam\u0131n\u0131, \u00f6zelliklerini ve olas\u0131l\u0131k fonksiyonunu hesaplaman\u0131n somut bir \u00f6rne\u011fini bulacaks\u0131n\u0131z. Ek olarak, bir olas\u0131l\u0131k fonksiyonu ile di\u011fer olas\u0131l\u0131ksal fonksiyon t\u00fcrleri aras\u0131ndaki farklar sunulmaktad\u0131r. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-funcion-de-probabilidad\"><\/span> Olas\u0131l\u0131k fonksiyonu nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Olas\u0131l\u0131k <strong>k\u00fctle<\/strong> <strong>fonksiyonu<\/strong> olarak da adland\u0131r\u0131lan olas\u0131l\u0131k fonksiyonu, ayr\u0131 bir rastgele de\u011fi\u015fkenin belirli bir de\u011feri alma olas\u0131l\u0131\u011f\u0131n\u0131 tan\u0131mlayan matematiksel bir fonksiyondur.<\/p>\n<p> Yani bir olas\u0131l\u0131k fonksiyonu, ayr\u0131k bir de\u011fi\u015fkenin bir de\u011fere tam olarak e\u015fit olma olas\u0131l\u0131\u011f\u0131n\u0131 d\u00f6nd\u00fcr\u00fcr.<\/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-d942818613a97133a923401de5479f3e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=P[X=x]\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"130\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u00d6rne\u011fin, bir zar at\u0131ld\u0131\u011f\u0131nda herhangi bir say\u0131n\u0131n gelme olas\u0131l\u0131\u011f\u0131 1\/6&#8217;d\u0131r (bir zar\u0131n alt\u0131 kenar\u0131 vard\u0131r), dolay\u0131s\u0131yla bu \u00f6rnek uzayla ili\u015fkili olas\u0131l\u0131k fonksiyonu, hangi de\u011fer olursa olsun n i\u00e7in 1\/6&#8217;ya e\u015fit olacakt\u0131r. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-la-funcion-de-probabilidad\"><\/span> Olas\u0131l\u0131k fonksiyonunun \u00f6zellikleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Olas\u0131l\u0131k fonksiyonlar\u0131 a\u015fa\u011f\u0131daki \u00f6zelliklere sahiptir:<\/p>\n<ul>\n<li> Olas\u0131l\u0131klar negatif olamaz, dolay\u0131s\u0131yla olas\u0131l\u0131k fonksiyonu 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> Ayn\u0131 \u015fekilde maksimum olas\u0131l\u0131k birliktir, yani olay her zaman meydana gelecektir. Bu nedenle olas\u0131l\u0131k 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> Son olarak, bir olas\u0131l\u0131k fonksiyonunun t\u00fcm de\u011ferlerinin toplam\u0131, \u00f6rnek uzaydaki t\u00fcm olas\u0131l\u0131klar\u0131n toplam\u0131 oldu\u011fundan 1 verir. <\/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-180b1dbe0de9d95eb7b2dc1372b4e2ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\sum_{i=1}^{+\\infty}f(x_i)=\\sum_{i=1}^{+\\infty}p_i=1\" title=\"Rendered by QuickLaTeX.com\" height=\"51\" width=\"167\" style=\"vertical-align: -21px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-funcion-de-probabilidad\"><\/span> Olas\u0131l\u0131k Fonksiyonu \u00d6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Art\u0131k olas\u0131l\u0131k fonksiyonunun tan\u0131m\u0131n\u0131 ve \u00f6zelliklerini bildi\u011fimize g\u00f6re, bu t\u00fcr olas\u0131l\u0131k fonksiyonunun bir \u00f6rne\u011fini g\u00f6relim.<\/p>\n<ul>\n<li> D\u00f6rt ba\u011f\u0131ms\u0131z yaz\u0131-tura at\u0131\u015f\u0131 yaparak 0, 1, 2, 3 ve 4 kez tura gelme olas\u0131l\u0131\u011f\u0131n\u0131 hesaplay\u0131n. Daha sonra bulunan olas\u0131l\u0131k fonksiyonunun grafi\u011fini \u00e7izin.<\/li>\n<\/ul>\n<p> \u00d6ncelikle tura gelme olas\u0131l\u0131klar\u0131n\u0131 hesaplamal\u0131y\u0131z, bunun i\u00e7in olas\u0131 vakalar\u0131 toplam vaka say\u0131s\u0131na b\u00f6lmeliyiz. T\u00fcm olas\u0131l\u0131klar\u0131n hesaplamas\u0131n\u0131 a\u015fa\u011f\u0131daki tabloda g\u00f6rebilirsiniz: <\/p>\n<figure class=\"wp-block-image 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 jeton \u00e7ekme oran\u0131\" class=\"wp-image-2346\" width=\"496\" height=\"334\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Ve t\u00fcm olas\u0131l\u0131klar\u0131 hesaplad\u0131ktan sonra olas\u0131l\u0131k fonksiyonunun de\u011ferlerini bir grafik \u00fczerinde g\u00f6sterebiliriz: <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/exemple-de-fonction-de-probabilite.png\" alt=\"olas\u0131l\u0131k fonksiyonu \u00f6rne\u011fi\" class=\"wp-image-2497\" width=\"476\" height=\"321\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> G\u00f6rd\u00fc\u011f\u00fcn\u00fcz gibi al\u0131\u015ft\u0131rmadaki olas\u0131l\u0131k fonksiyonu, t\u00fcm de\u011ferleri 0 ile 1 aras\u0131nda oldu\u011fundan ve \u00fcstelik t\u00fcm de\u011ferlerinin toplam\u0131 1&#8217;e e\u015fit oldu\u011fundan olas\u0131l\u0131k fonksiyonlar\u0131n\u0131n t\u00fcm \u00f6zelliklerini kar\u015f\u0131lamaktad\u0131r. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"funcion-de-probabilidad-y-funcion-de-densidad\"><\/span> Olas\u0131l\u0131k fonksiyonu ve yo\u011funluk fonksiyonu<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bu b\u00f6l\u00fcmde olas\u0131l\u0131k fonksiyonu ile yo\u011funluk fonksiyonu aras\u0131ndaki fark\u0131 g\u00f6rece\u011fiz \u00e7\u00fcnk\u00fc bunlar ayn\u0131 amaca sahip ancak farkl\u0131 durumlarda kullan\u0131lan iki t\u00fcr olas\u0131l\u0131k fonksiyonudur.<\/p>\n<p> <strong>Olas\u0131l\u0131k fonksiyonu ile yo\u011funluk fonksiyonu aras\u0131ndaki fark,<\/strong> olas\u0131l\u0131klar\u0131n tan\u0131mlad\u0131\u011f\u0131 de\u011fi\u015fken t\u00fcr\u00fcd\u00fcr. Olas\u0131l\u0131k fonksiyonu ayr\u0131k bir de\u011fi\u015fkenin olas\u0131l\u0131klar\u0131n\u0131 tan\u0131mlamak i\u00e7in kullan\u0131l\u0131rken, yo\u011funluk fonksiyonu s\u00fcrekli bir de\u011fi\u015fkenin olas\u0131l\u0131klar\u0131n\u0131 tan\u0131mlamak i\u00e7in kullan\u0131l\u0131r.<\/p>\n<p> Dolay\u0131s\u0131yla de\u011fi\u015fkene ba\u011fl\u0131 olarak bir olas\u0131l\u0131k fonksiyonu veya yo\u011funluk fonksiyonu kullan\u0131l\u0131r.<\/p>\n<p> Yo\u011funluk i\u015flevi 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\/yogunluk-fonksiyonu\/\">olas\u0131l\u0131k yo\u011funluk fonksiyonu<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"funcion-de-probabilidad-y-funcion-de-distribucion\"><\/span> Olas\u0131l\u0131k fonksiyonu ve da\u011f\u0131l\u0131m fonksiyonu<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Bir olas\u0131l\u0131k fonksiyonu ile bir da\u011f\u0131l\u0131m fonksiyonu aras\u0131ndaki fark,<\/strong> tan\u0131mlad\u0131klar\u0131 olas\u0131l\u0131k t\u00fcr\u00fcd\u00fcr. Olas\u0131l\u0131k fonksiyonu de\u011fi\u015fkenin belirli bir de\u011fer alma olas\u0131l\u0131\u011f\u0131n\u0131 belirtirken, da\u011f\u0131l\u0131m fonksiyonu de\u011fi\u015fkenin k\u00fcm\u00fclatif olas\u0131l\u0131\u011f\u0131n\u0131 a\u00e7\u0131klar.<\/p>\n<p> Bu nedenle da\u011f\u0131l\u0131m fonksiyonu olas\u0131l\u0131k fonksiyonundan hesaplan\u0131r.<\/p>\n<p> \u00d6rnek olarak a\u015fa\u011f\u0131daki ba\u011flant\u0131da, yukar\u0131daki al\u0131\u015ft\u0131rmada bulunan olas\u0131l\u0131k fonksiyonuna dayal\u0131 olarak, d\u00f6rt yaz\u0131-tura at\u0131ld\u0131\u011f\u0131nda tura gelmesine y\u00f6nelik da\u011f\u0131t\u0131m fonksiyonunun hesaplanmas\u0131n\u0131 g\u00f6rebilirsiniz. <\/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 \u00f6rne\u011fi<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede olas\u0131l\u0131k fonksiyonlar\u0131n\u0131n ne oldu\u011fu a\u00e7\u0131klanmaktad\u0131r. B\u00f6ylece olas\u0131l\u0131k fonksiyonunun anlam\u0131n\u0131, \u00f6zelliklerini ve olas\u0131l\u0131k fonksiyonunu hesaplaman\u0131n somut bir \u00f6rne\u011fini bulacaks\u0131n\u0131z. Ek olarak, bir olas\u0131l\u0131k fonksiyonu ile di\u011fer olas\u0131l\u0131ksal fonksiyon t\u00fcrleri aras\u0131ndaki farklar sunulmaktad\u0131r. Olas\u0131l\u0131k fonksiyonu nedir? Olas\u0131l\u0131k k\u00fctle fonksiyonu olarak da adland\u0131r\u0131lan olas\u0131l\u0131k fonksiyonu, ayr\u0131 bir rastgele de\u011fi\u015fkenin belirli bir de\u011feri alma olas\u0131l\u0131\u011f\u0131n\u0131 tan\u0131mlayan matematiksel [&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-118","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>Olas\u0131l\u0131k fonksiyonu nedir? 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