{"id":227,"date":"2023-08-03T23:08:41","date_gmt":"2023-08-03T23:08:41","guid":{"rendered":"https:\/\/statorials.org\/tr\/duzgun-surekli-dagitim\/"},"modified":"2023-08-03T23:08:41","modified_gmt":"2023-08-03T23:08:41","slug":"duzgun-surekli-dagitim","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/duzgun-surekli-dagitim\/","title":{"rendered":"D\u00fczg\u00fcn ve s\u00fcrekli da\u011f\u0131t\u0131m"},"content":{"rendered":"

Bu makalede s\u00fcrekli d\u00fczg\u00fcn da\u011f\u0131l\u0131m\u0131n ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. Ayr\u0131ca s\u00fcrekli d\u00fczg\u00fcn da\u011f\u0131l\u0131m\u0131n grafi\u011fini ve bu t\u00fcr da\u011f\u0131l\u0131m\u0131n \u00f6zelliklerini de bulacaks\u0131n\u0131z. <\/p>\n

<\/span> S\u00fcrekli d\u00fczg\u00fcn da\u011f\u0131l\u0131m nedir?<\/span><\/h2>\n

S\u00fcrekli d\u00fczg\u00fcn da\u011f\u0131l\u0131m,<\/strong> t\u00fcm de\u011ferlerin ayn\u0131 olu\u015fma olas\u0131l\u0131\u011f\u0131na sahip oldu\u011fu bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 t\u00fcr\u00fcd\u00fcr. Ba\u015fka bir deyi\u015fle s\u00fcrekli d\u00fczg\u00fcn da\u011f\u0131l\u0131m, olas\u0131l\u0131\u011f\u0131n belirli bir aral\u0131kta d\u00fczg\u00fcn da\u011f\u0131ld\u0131\u011f\u0131 bir da\u011f\u0131l\u0131md\u0131r.<\/p>\n

S\u00fcrekli d\u00fczg\u00fcn da\u011f\u0131l\u0131m, sabit olas\u0131l\u0131\u011fa sahip s\u00fcrekli de\u011fi\u015fkenleri tan\u0131mlamak i\u00e7in kullan\u0131l\u0131r. Benzer \u015fekilde, rastgele s\u00fcre\u00e7leri tan\u0131mlamak i\u00e7in s\u00fcrekli tekd\u00fcze da\u011f\u0131l\u0131m kullan\u0131l\u0131r, \u00e7\u00fcnk\u00fc t\u00fcm sonu\u00e7lar\u0131n ayn\u0131 olas\u0131l\u0131\u011fa sahip olmas\u0131, sonu\u00e7ta rastgelelik oldu\u011fu anlam\u0131na gelir.<\/p>\n

S\u00fcrekli d\u00fczg\u00fcn da\u011f\u0131l\u0131m, e\u015f olas\u0131l\u0131k aral\u0131\u011f\u0131n\u0131 tan\u0131mlayan a<\/em> ve b<\/em> olmak \u00fczere iki karakteristik parametreye sahiptir. Dolay\u0131s\u0131yla s\u00fcrekli d\u00fczg\u00fcn da\u011f\u0131l\u0131m\u0131n sembol\u00fc U(a,b)’<\/em> dir; burada a<\/em> ve b<\/em> , da\u011f\u0131l\u0131m\u0131n karakteristik de\u011ferleridir.<\/p>\n<\/p>\n

\"X\\sim<\/p>\n<\/p>\n

\u00d6rne\u011fin, rastgele bir deneyin sonucu 5 ile 9 aras\u0131nda herhangi bir de\u011fer alabiliyorsa ve olas\u0131 t\u00fcm sonu\u00e7lar\u0131n olu\u015fma olas\u0131l\u0131\u011f\u0131 ayn\u0131ysa, deney s\u00fcrekli d\u00fczg\u00fcn da\u011f\u0131l\u0131m U(5.9) ile sim\u00fcle edilebilir.<\/p>\n

S\u00fcrekli d\u00fczg\u00fcn da\u011f\u0131l\u0131ma dikd\u00f6rtgen da\u011f\u0131l\u0131m<\/strong> da denir. <\/p>\n

<\/span> S\u00fcrekli d\u00fczg\u00fcn da\u011f\u0131t\u0131m form\u00fcl\u00fc<\/span><\/h2>\n

D\u00fczg\u00fcn bir da\u011f\u0131l\u0131m olas\u0131l\u0131\u011f\u0131n\u0131 tan\u0131mlayan yo\u011funluk fonksiyonu, b<\/em> ile a<\/em> aras\u0131ndaki farka b\u00f6l\u00fcn\u00fcr. Bu nedenle s\u00fcrekli d\u00fczg\u00fcn da\u011f\u0131l\u0131m form\u00fcl\u00fc<\/strong> \u015fu \u015fekildedir:<\/p>\n<\/p>\n

\"\\begin{array}{c}X\\sim<\/p>\n<\/p>\n

\u00d6te yandan s\u00fcrekli d\u00fczg\u00fcn da\u011f\u0131l\u0131m\u0131n k\u00fcm\u00fclatif olas\u0131l\u0131k fonksiyonu a\u015fa\u011f\u0131daki ifadeyle tan\u0131mlan\u0131r:<\/p>\n

 *** QuickLaTeX cannot compile formula:\n\\displaystyle F(x)=\\left\\{\\begin{array}{ll}0&\\text{si }x<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id =\"grafica-de-la-distribucion-uniforme-continua\"><\/span> Graph of continuous uniform distribution<span class=\"ez-toc-section-end\"><\/span><\/h2> Since in a distribution uniform continuous probability is constant, its graphical representation is simply a function with a constant value defined in the same interval as the uniform distribution. <figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/ 08\/distribution-uniforme-continue.png\" alt=\"Continuous uniform distribution graph\" class=\"wp-image-4498\" width=\"330\" height=\"232\" srcset=\"\" sizes=\"\"><\/figure > On the other hand, the cumulative probability graph of the continuous uniform distribution is as follows: <figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-uniforme-continue-probabilite-cumulative.png\" alt=\"cumulative probability plot of a continuous uniform distribution\" class= \"wp-image-4499\" width=\"247\" height=\"193\" srcset=\"\" sizes=\"\"><\/figure><h2 class=\"wp-block-heading\"><span class=\"ez-toc -section\" id=\"caracteristicas-de-la-distribucion-uniforme-continua\"><\/span> Characteristics of the continuous uniform distribution<span class=\"ez-toc-section-end\"><\/span><\/h2 > The continuous uniform distribution has the following characteristics: <ul><li> The continuous uniform distribution is defined by two real parameters, <em>a<\/em> and <em>b<\/em>, which establish the limits in which the probability is constant.<\/li><\/ul>[latex]a,b\\in \\mathbb{R}\n\n***Error message:\nPlease use \\mathaccent for accents in math mode.\nleading text: ...continuous uniform distribution probability\nPlease use \\mathaccent for accents in math mode.\nleading text: ...if the probability is constant, its representation\nPlease use \\mathaccent for accents in math mode.\nleading text: ...a function with a constant value de\nPlease use \\mathaccent for accents in math mode.\nleading text: ...c a constant value defined in the same\nPlease use \\mathaccent for accents in math mode.\nleading text: ...On the other hand, the probability graph\nPlease use \\mathaccent for accents in math mode.\nleading text: ... part, the cumulative probability graph\nPlease use \\mathaccent for accents in math mode.\nleading text: ...nue-probabilite-cumulative.png\" alt=\"plot\n\n<\/pre>\n