{"id":226,"date":"2023-08-03T23:26:42","date_gmt":"2023-08-03T23:26:42","guid":{"rendered":"https:\/\/statorials.org\/tr\/ayrik-duzgun-dagilim\/"},"modified":"2023-08-03T23:26:42","modified_gmt":"2023-08-03T23:26:42","slug":"ayrik-duzgun-dagilim","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ayrik-duzgun-dagilim\/","title":{"rendered":"Ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131m"},"content":{"rendered":"<p>Bu makale ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131m\u0131n ne oldu\u011funu ve karakteristik form\u00fcl\u00fcn\u00fcn ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. Ayn\u0131 \u015fekilde ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131m\u0131n grafiksel g\u00f6sterimini ve \u00f6zelliklerinin neler oldu\u011funu g\u00f6rebileceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-uniforme-discreta\"><\/span> Ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131m nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Ayr\u0131k tekd\u00fcze da\u011f\u0131l\u0131m,<\/strong> t\u00fcm de\u011ferlerin e\u015f olas\u0131l\u0131kl\u0131 oldu\u011fu, yani ayr\u0131k bir tekd\u00fcze da\u011f\u0131l\u0131mda t\u00fcm de\u011ferlerin ayn\u0131 olu\u015fma olas\u0131l\u0131\u011f\u0131na sahip oldu\u011fu ayr\u0131 bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r.<\/p>\n<p> \u00d6rne\u011fin, t\u00fcm olas\u0131 sonu\u00e7lar\u0131n (1, 2, 3, 4, 5 veya 6) ayn\u0131 olu\u015fma olas\u0131l\u0131\u011f\u0131na sahip olmas\u0131 nedeniyle, bir zar\u0131n at\u0131lmas\u0131 ayr\u0131k ve d\u00fczg\u00fcn bir da\u011f\u0131l\u0131mla tan\u0131mlanabilir.<\/p>\n<p> Genel olarak, ayr\u0131k bir d\u00fczg\u00fcn da\u011f\u0131l\u0131m, da\u011f\u0131l\u0131m\u0131n alabilece\u011fi olas\u0131 de\u011ferlerin aral\u0131\u011f\u0131n\u0131 tan\u0131mlayan <em>a<\/em> ve <em>b<\/em> olmak \u00fczere iki karakteristik parametreye sahiptir. Bu nedenle, bir de\u011fi\u015fken ayr\u0131k bir d\u00fczg\u00fcn da\u011f\u0131l\u0131mla tan\u0131mland\u0131\u011f\u0131nda, <em>D\u00fczg\u00fcn(a,b)<\/em> olarak yaz\u0131l\u0131r.<\/p>\n<p> Ayr\u0131k tekd\u00fcze da\u011f\u0131l\u0131m, rastgele deneyleri tan\u0131mlamak i\u00e7in kullan\u0131labilir \u00e7\u00fcnk\u00fc t\u00fcm sonu\u00e7lar\u0131n ayn\u0131 olas\u0131l\u0131\u011fa sahip olmas\u0131, deneyin rastgele oldu\u011fu anlam\u0131na gelir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-distribucion-uniforme-discreta\"><\/span> Ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131m form\u00fcl\u00fc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Art\u0131k ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131m\u0131n tan\u0131m\u0131n\u0131 bildi\u011fimize g\u00f6re, bu t\u00fcr bir da\u011f\u0131l\u0131m\u0131n de\u011ferlerinin ortaya \u00e7\u0131kma olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamam\u0131z\u0131 sa\u011flayan form\u00fcl\u00fcn ne oldu\u011funu g\u00f6rece\u011fiz.<\/p>\n<p> Ayr\u0131k bir d\u00fczg\u00fcn da\u011f\u0131l\u0131m\u0131n olas\u0131l\u0131k fonksiyonu sabittir ve de\u011feri, olas\u0131 sonu\u00e7lar\u0131n toplam say\u0131s\u0131 \u00fczerinden bire e\u015fittir. Dolay\u0131s\u0131yla <strong>ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131m form\u00fcl\u00fc<\/strong> 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-e859f9b02aa8706b23092d8119ab3c82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P[X=x]=\\cfrac{1}{n}=\\cfrac{1}{b-a+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"205\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> \u00d6te yandan ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131m\u0131n k\u00fcm\u00fclatif olas\u0131l\u0131k fonksiyonunun form\u00fcl\u00fc 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-1e504fea34915fd188d59fac9efd70ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P[X\\leq x]=\\cfrac{\\lfloor x \\rfloor -a + 1}{b-a+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"187\" style=\"vertical-align: -14px;\"><\/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-0e55b0b3943237ccfc96979505679274_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> Ve<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ad69adf868bc701e561aa555db995f1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131m\u0131n karakteristik parametreleridir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-uniforme-discreta\"><\/span> Ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131t\u0131m diyagram\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131m bir aral\u0131kta yaln\u0131zca belirli de\u011ferleri alabildi\u011finden grafiksel g\u00f6sterimi noktalardan olu\u015fur. Ayr\u0131ca, t\u00fcm olas\u0131l\u0131klar e\u015fittir, dolay\u0131s\u0131yla ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131mdaki t\u00fcm noktalar ayn\u0131 dikey koordinata sahiptir. <\/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\/distribution-uniforme-et-discrete.png\" alt=\"Ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131t\u0131m diyagram\u0131\" class=\"wp-image-4516\" width=\"334\" height=\"234\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> \u00d6te yandan ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131m\u0131n k\u00fcm\u00fclatif olas\u0131l\u0131k grafi\u011fi \u015fu \u015fekildedir: <\/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\/distribution-uniforme-discrete-a-probabilite-cumulative.png\" alt=\"ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131m\u0131n k\u00fcm\u00fclatif olas\u0131l\u0131\u011f\u0131\" class=\"wp-image-4520\" width=\"253\" height=\"225\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-uniforme-discreta\"><\/span> Ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131m\u0131n \u00f6zellikleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131m a\u015fa\u011f\u0131daki \u00f6zelliklere sahiptir:<\/p>\n<ul>\n<li> Ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131m, da\u011f\u0131l\u0131m\u0131n olas\u0131 de\u011ferlerinin aral\u0131\u011f\u0131n\u0131 belirleyen <em>a<\/em> ve <em>b<\/em> olmak \u00fczere iki tamsay\u0131 parametresi ile tan\u0131mlan\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-4937817442028ed33c270680f7eb4664_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c} X\\sim \\text{Uniforme}(a,b)\\\\[2ex]b\\geq a\\\\[2ex]n=b-a+1\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"91\" width=\"150\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Ayr\u0131k bir d\u00fczg\u00fcn da\u011f\u0131l\u0131m\u0131n ortalamas\u0131, iki karakteristik parametresinin toplam\u0131n\u0131n ikiye b\u00f6l\u00fcnmesine 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-96d92a77b5dce5d38b2b2f3b79ac09a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E[X]=\\cfrac{a+b}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"105\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> Ayr\u0131k bir d\u00fczg\u00fcn da\u011f\u0131l\u0131m\u0131n medyan\u0131, ortalamas\u0131na e\u015fde\u011ferdir, dolay\u0131s\u0131yla ayn\u0131 ifadeyle 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-9acd8c7117f5765f6e47060148e541e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Me=\\cfrac{a+b}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"92\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> Ayr\u0131k bir d\u00fczg\u00fcn da\u011f\u0131l\u0131m\u0131n varyans\u0131, toplam sonu\u00e7 say\u0131s\u0131n\u0131n karesinden eksi bir b\u00f6l\u00fc on ikiye 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-588e02469dd6ee652f7a648225f6e13c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(X)=\\cfrac{n^2-1}{12}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"137\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> Ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131m, ortalamas\u0131na g\u00f6re simetriktir, dolay\u0131s\u0131yla bu olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n \u00e7arp\u0131kl\u0131k katsay\u0131s\u0131 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-f32c2fb2ba717dc1c88c67cb82c26e9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A=0\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"46\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131m\u0131n bas\u0131kl\u0131\u011f\u0131 a\u015fa\u011f\u0131daki ifade kullan\u0131larak hesaplanabilir: <\/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-7d978558a3607d6eee4b26d8a38fe3a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C=-\\cfrac{6\\cdot (n^2+1)}{5\\cdot (n^2+1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"138\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"distribucion-uniforme-discreta-y-distribucion-uniforme-continua\"><\/span> Ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131m ve s\u00fcrekli d\u00fczg\u00fcn da\u011f\u0131l\u0131m<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Son olarak, ayr\u0131k bir d\u00fczg\u00fcn da\u011f\u0131l\u0131m ile s\u00fcrekli bir tekd\u00fcze da\u011f\u0131l\u0131m aras\u0131ndaki fark\u0131n ne oldu\u011funu g\u00f6rece\u011fiz, \u00e7\u00fcnk\u00fc bunlar iki benzer t\u00fcr olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r, ancak \u00f6nemli bir fark vard\u0131r.<\/p>\n<p> <strong>Ayr\u0131k bir d\u00fczg\u00fcn da\u011f\u0131l\u0131m ile s\u00fcrekli bir tekd\u00fcze da\u011f\u0131l\u0131m aras\u0131ndaki fark,<\/strong> bunlar\u0131n olas\u0131 de\u011ferlerinde yatmaktad\u0131r. Ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131m bir aral\u0131kta yaln\u0131zca belirli de\u011ferleri alabilirken, s\u00fcrekli d\u00fczg\u00fcn da\u011f\u0131l\u0131m tan\u0131mland\u0131\u011f\u0131 aral\u0131ktaki herhangi bir de\u011feri alabilir.<\/p>\n<p> Genel olarak, ayr\u0131k tekd\u00fcze da\u011f\u0131l\u0131mlar yaln\u0131zca tam say\u0131 de\u011ferleri alabilirken, s\u00fcrekli tekd\u00fcze da\u011f\u0131l\u0131mlar da ondal\u0131k de\u011ferler alabilir. <\/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\/duzgun-surekli-dagitim\/\">S\u00fcrekli d\u00fczg\u00fcn da\u011f\u0131l\u0131m<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu makale ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131m\u0131n ne oldu\u011funu ve karakteristik form\u00fcl\u00fcn\u00fcn ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. Ayn\u0131 \u015fekilde ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131m\u0131n grafiksel g\u00f6sterimini ve \u00f6zelliklerinin neler oldu\u011funu g\u00f6rebileceksiniz. Ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131m nedir? Ayr\u0131k tekd\u00fcze da\u011f\u0131l\u0131m, t\u00fcm de\u011ferlerin e\u015f olas\u0131l\u0131kl\u0131 oldu\u011fu, yani ayr\u0131k bir tekd\u00fcze da\u011f\u0131l\u0131mda t\u00fcm de\u011ferlerin ayn\u0131 olu\u015fma olas\u0131l\u0131\u011f\u0131na sahip oldu\u011fu ayr\u0131 bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r. \u00d6rne\u011fin, t\u00fcm [&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-226","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 Ayr\u0131k tekd\u00fcze da\u011f\u0131l\u0131m - Olas\u0131l\u0131k ve istatistik<\/title>\n<meta name=\"description\" content=\"Bu makale ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131m\u0131n ne oldu\u011funu ve karakteristik form\u00fcl\u00fcn\u00fcn ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. 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