{"id":769,"date":"2023-07-28T20:00:37","date_gmt":"2023-07-28T20:00:37","guid":{"rendered":"https:\/\/statorials.org\/tr\/cok-terimli-dagilim\/"},"modified":"2023-07-28T20:00:37","modified_gmt":"2023-07-28T20:00:37","slug":"cok-terimli-dagilim","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/cok-terimli-dagilim\/","title":{"rendered":"\u00c7ok terimli da\u011f\u0131t\u0131ma giri\u015f"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>\u00c7ok terimli da\u011f\u0131l\u0131m,<\/strong> her sonucun sabit bir ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131na sahip oldu\u011fu durumda, <em>k<\/em> farkl\u0131 sonu\u00e7 i\u00e7in belirli say\u0131da say\u0131m elde etme olas\u0131l\u0131\u011f\u0131n\u0131 a\u00e7\u0131klar.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><sub>E\u011fer<\/sub> <sub>bir<\/sub> <em>rastgele<\/em> <a href=\"https:\/\/statorials.org\/tr\/rastgele-degiskenler\/\" target=\"_blank\" rel=\"noopener\">de\u011fi\u015fken<\/a> <sub>_<\/sub> a\u015fa\u011f\u0131daki form\u00fclle bulunabilirse:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Olas\u0131l\u0131k =<\/strong> <strong>n! * (p <sub>1<\/sub> <sup>x <sub>1<\/sub><\/sup> * p <sub>2<\/sub> <sup>x <sub>2<\/sub><\/sup> * \u2026 * p <sub>k<\/sub> <sup>x <sub>k<\/sub><\/sup> ) \/ (x <sub>1<\/sub> ! * x <sub>2<\/sub> ! \u2026 * x <sub>k<\/sub> !)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> toplam olay say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x <sub>1<\/sub> :<\/strong> sonu\u00e7 1&#8217;in olu\u015fma say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p <sub>1<\/sub> :<\/strong> belirli bir denemede sonu\u00e7 1&#8217;in ortaya \u00e7\u0131kma olas\u0131l\u0131\u011f\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin bir torbada 5 k\u0131rm\u0131z\u0131, 3 ye\u015fil ve 2 mavi bilye oldu\u011funu varsayal\u0131m. Torbadan rastgele 5 bilyeyi yerine koyarak \u00e7ekersek, tam olarak 2 k\u0131rm\u0131z\u0131, 2 ye\u015fil ve 1 mavi bilye elde etme olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu soruyu cevaplamak i\u00e7in \u00e7ok terimli da\u011f\u0131l\u0131m\u0131 a\u015fa\u011f\u0131daki parametrelerle kullanabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>say\u0131<\/strong> : 5<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x <sub>1<\/sub><\/strong> (# k\u0131rm\u0131z\u0131 bilyeler) = 2,<\/span> <span style=\"color: #000000;\"><strong>x <sub>2<\/sub><\/strong> (# ye\u015fil bilyeler) = 2,<\/span> <span style=\"color: #000000;\"><strong>x <sub>3<\/sub><\/strong> (# mavi bilyeler) = 1<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p <sub>1<\/sub><\/strong> (k\u0131rm\u0131z\u0131 olas\u0131l\u0131k) = 0,5,<\/span> <span style=\"color: #000000;\"><strong>p <sub>2<\/sub><\/strong> (ye\u015fil olas\u0131l\u0131k) = 0,3,<\/span> <span style=\"color: #000000;\"><strong>p <sub>3<\/sub><\/strong> (mavi olas\u0131l\u0131k) = 0,2<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu say\u0131lar\u0131 form\u00fcle yerle\u015ftirdi\u011fimizde olas\u0131l\u0131\u011f\u0131n \u015f\u00f6yle oldu\u011funu buluruz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Olas\u0131l\u0131k<\/strong> = 5! * (0,5 <sup>2<\/sup> * 0,3 <sup>2<\/sup> * 0,2 <sup>1<\/sup> ) \/ (2! * 2! * 1!) = <strong>0,135<\/strong> .<\/span><\/p>\n<h2> <strong>\u00c7ok Terimli Da\u011f\u0131t\u0131m Uygulama Problemleri<\/strong><\/h2>\n<p> <span style=\"color: #000000;\">\u00c7ok terimli da\u011f\u0131l\u0131ma ili\u015fkin bilginizi test etmek i\u00e7in a\u015fa\u011f\u0131daki al\u0131\u015ft\u0131rma problemlerini kullan\u0131n.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em><strong>Not:<\/strong> Bu sorular\u0131n cevaplar\u0131n\u0131 hesaplamak i\u00e7in <a href=\"https:\/\/statorials.org\/tr\/cok-terimli-dagilim-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">Multinomial Da\u011f\u0131l\u0131m Hesaplay\u0131c\u0131y\u0131<\/a> kullanaca\u011f\u0131z.<\/em><\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Sorun 1<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>Soru:<\/strong> \u00dc\u00e7l\u00fc belediye ba\u015fkanl\u0131\u011f\u0131 se\u00e7iminde A aday\u0131 y\u00fczde 10, B aday\u0131 y\u00fczde 40, C aday\u0131 y\u00fczde 50 oy al\u0131yor. 10 se\u00e7menden olu\u015fan rastgele bir \u00f6rneklem se\u00e7ersek, 2 ki\u015finin A aday\u0131na, 4 ki\u015finin B aday\u0131na ve 4 ki\u015finin C aday\u0131na oy verme olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\"><strong>Cevap:<\/strong> Multinomial Da\u011f\u0131l\u0131m Hesaplay\u0131c\u0131s\u0131n\u0131 a\u015fa\u011f\u0131daki girdilerle kullanarak olas\u0131l\u0131\u011f\u0131n <strong>0,0504 oldu\u011funu buluyoruz:<\/strong><\/span> <\/p>\n<p data-slot-rendered-dynamic=\"true\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8244 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/multinomialcalc1.png\" alt=\"\u00c7ok Terimli Hesap Makinesi \u00d6rne\u011fi\" width=\"260\" height=\"553\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Sorun 2<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>Soru:<\/strong> Bir vazoda 6 sar\u0131 bilye, 2 k\u0131rm\u0131z\u0131 bilye ve 2 pembe bilye bulundu\u011funu varsayal\u0131m. Torbadan rastgele 4 top se\u00e7ersek ve yerine koyarsak, 4 topun da sar\u0131 olma olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\"><strong>Cevap:<\/strong> Multinomial Da\u011f\u0131l\u0131m Hesaplay\u0131c\u0131s\u0131n\u0131 a\u015fa\u011f\u0131daki girdilerle kullanarak olas\u0131l\u0131\u011f\u0131n <strong>0,1296 oldu\u011funu buluyoruz:<\/strong><\/span> <\/p>\n<p data-slot-rendered-dynamic=\"true\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8246 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/multinomialcalc2.png\" alt=\"\u00c7ok Terimli Olas\u0131l\u0131k Da\u011f\u0131l\u0131m\u0131 \u00d6rne\u011fi\" width=\"261\" height=\"561\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Sorun 3<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>Soru:<\/strong> \u0130ki \u00f6\u011frencinin birbirlerine kar\u015f\u0131 satran\u00e7 oynad\u0131\u011f\u0131n\u0131 varsayal\u0131m. A \u00f6\u011frencisinin belirli bir oyunu kazanma olas\u0131l\u0131\u011f\u0131 0,5, B \u00f6\u011frencisinin belirli bir oyunu kazanma olas\u0131l\u0131\u011f\u0131 0,3 ve belirli bir oyunda beraberlik olma olas\u0131l\u0131\u011f\u0131 0, 2&#8217;dir. E\u011fer 10 oyun oynarlarsa, A oyuncusunun 4 kez kazanmas\u0131, B oyuncusunun 5 kez kazanmas\u0131 ve 1 kez berabere kalmas\u0131 olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\"><strong>Cevap:<\/strong> Multinomial Da\u011f\u0131l\u0131m Hesaplay\u0131c\u0131s\u0131n\u0131 a\u015fa\u011f\u0131daki girdilerle kullanarak olas\u0131l\u0131\u011f\u0131n <strong>0,038272 oldu\u011funu buluyoruz:<\/strong><\/span> <\/p>\n<p data-slot-rendered-dynamic=\"true\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8247 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/multinomialcalc3.png\" alt=\"\u00c7ok Terimli Da\u011f\u0131l\u0131m \u00d6rne\u011fi\" width=\"259\" height=\"544\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3 data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimler istatistikteki di\u011fer yayg\u0131n da\u011f\u0131l\u0131mlara bir giri\u015f sa\u011flar:<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> Normal da\u011f\u0131l\u0131ma giri\u015f<br \/> <a href=\"https:\/\/statorials.org\/tr\/binom-dagilimi-1\/\" target=\"_blank\" rel=\"noopener\">Binom da\u011f\u0131l\u0131m\u0131na giri\u015f<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/balik-dagitimi\/\" target=\"_blank\" rel=\"noopener\">Poisson da\u011f\u0131l\u0131m\u0131na giri\u015f<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/geometrik-dagilim\/\" target=\"_blank\" rel=\"noopener\">Geometrik da\u011f\u0131l\u0131ma giri\u015f<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00c7ok terimli da\u011f\u0131l\u0131m, her sonucun sabit bir ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131na sahip oldu\u011fu durumda, k farkl\u0131 sonu\u00e7 i\u00e7in belirli say\u0131da say\u0131m elde etme olas\u0131l\u0131\u011f\u0131n\u0131 a\u00e7\u0131klar. E\u011fer bir rastgele de\u011fi\u015fken _ a\u015fa\u011f\u0131daki form\u00fclle bulunabilirse: Olas\u0131l\u0131k = n! * (p 1 x 1 * p 2 x 2 * \u2026 * p k x k ) \/ (x 1 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-769","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u00c7ok Terimli Da\u011f\u0131l\u0131ma Giri\u015f - Statorials<\/title>\n<meta name=\"description\" content=\"Resmi bir tan\u0131m ve birka\u00e7 \u00f6rnek i\u00e7eren \u00e7ok terimli da\u011f\u0131l\u0131ma basit bir giri\u015f.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/tr\/cok-terimli-dagilim\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u00c7ok Terimli Da\u011f\u0131l\u0131ma Giri\u015f - Statorials\" \/>\n<meta property=\"og:description\" content=\"Resmi bir tan\u0131m ve birka\u00e7 \u00f6rnek i\u00e7eren \u00e7ok terimli da\u011f\u0131l\u0131ma basit bir giri\u015f.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/cok-terimli-dagilim\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-28T20:00:37+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/multinomialcalc1.png\" \/>\n<meta name=\"author\" content=\"Dr.benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr.benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/cok-terimli-dagilim\/\",\"url\":\"https:\/\/statorials.org\/tr\/cok-terimli-dagilim\/\",\"name\":\"\u00c7ok Terimli Da\u011f\u0131l\u0131ma Giri\u015f - Statorials\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-07-28T20:00:37+00:00\",\"dateModified\":\"2023-07-28T20:00:37+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Resmi bir tan\u0131m ve birka\u00e7 \u00f6rnek i\u00e7eren \u00e7ok terimli da\u011f\u0131l\u0131ma basit bir giri\u015f.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/cok-terimli-dagilim\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/cok-terimli-dagilim\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/cok-terimli-dagilim\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u00c7ok terimli da\u011f\u0131t\u0131ma giri\u015f\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/tr\/#website\",\"url\":\"https:\/\/statorials.org\/tr\/\",\"name\":\"Statorials\",\"description\":\"\u0130statistik okuryazarl\u0131\u011f\u0131 rehberiniz!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/tr\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"tr\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\",\"name\":\"Dr.benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"tr\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr.benjamin anderson\"},\"description\":\"Merhaba, ben Benjamin, emekli bir istatistik profes\u00f6r\u00fc ve Statorials \u00f6\u011fretmenine d\u00f6n\u00fc\u015ft\u00fcm. \u0130statistik alan\u0131ndaki kapsaml\u0131 deneyimim ve uzmanl\u0131\u011f\u0131mla, \u00f6\u011frencilerimi Statorials arac\u0131l\u0131\u011f\u0131yla g\u00fc\u00e7lendirmek i\u00e7in bilgilerimi payla\u015fmaya can at\u0131yorum. 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