{"id":768,"date":"2023-07-28T20:06:46","date_gmt":"2023-07-28T20:06:46","guid":{"rendered":"https:\/\/statorials.org\/tr\/negatif-binom-dagilimi\/"},"modified":"2023-07-28T20:06:46","modified_gmt":"2023-07-28T20:06:46","slug":"negatif-binom-dagilimi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/negatif-binom-dagilimi\/","title":{"rendered":"Negatif binom da\u011f\u0131l\u0131m\u0131na giri\u015f"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Negatif binom da\u011f\u0131l\u0131m\u0131,<\/strong> bir dizi Bernoulli denemesinde belirli say\u0131da ba\u015far\u0131 elde edilmeden \u00f6nce belirli say\u0131da ba\u015far\u0131s\u0131zl\u0131\u011f\u0131n ya\u015fanma olas\u0131l\u0131\u011f\u0131n\u0131 tan\u0131mlar.<\/span><\/p>\n<blockquote>\n<p> <span style=\"color: #000000;\">Bir <strong>Bernoulli denemesi<\/strong> yaln\u0131zca iki olas\u0131 sonucu olan bir deneydir \u2013 \u201cba\u015far\u0131l\u0131\u201d veya \u201cba\u015far\u0131s\u0131z\u201d ve ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 deney her yap\u0131ld\u0131\u011f\u0131nda ayn\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bernoulli makalesinin bir \u00f6rne\u011fi yaz\u0131 tura atmakt\u0131r. Para yaln\u0131zca iki tura gelebilir (turalara &#8220;vuru\u015f&#8221;, yaz\u0131lara ise &#8220;ba\u015far\u0131s\u0131zl\u0131k&#8221; diyebiliriz) ve paran\u0131n adil oldu\u011funu varsayarsak, her at\u0131\u015fta ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 0,5&#8217;tir.<\/span><\/p>\n<\/blockquote>\n<p> <span style=\"color: #000000;\"><em>Rastgele<\/em> <em>bir<\/em> <a href=\"https:\/\/statorials.org\/tr\/rastgele-degiskenler\/\" target=\"_blank\" rel=\"noopener\">de\u011fi\u015fken<\/a> <i>ise<\/i><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=k) =<\/strong> <strong><sub>k+r-1<\/sub> C <sub>k<\/sub> * (1-p) <sup>r<\/sup> *p <sup>k<\/sup><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>k:<\/strong> ar\u0131za say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>r:<\/strong> ba\u015far\u0131 say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p:<\/strong> belirli bir denemede ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sub>k+r-1<\/sub> C <sub>k<\/sub> :<\/strong> k kerede al\u0131nan (k+r-1) \u015feylerin kombinasyon say\u0131s\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, yaz\u0131 tura att\u0131\u011f\u0131m\u0131z\u0131 ve &#8220;ba\u015far\u0131l\u0131&#8221; bir olay\u0131 tura gelmek olarak tan\u0131mlad\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m. Toplam 4 ba\u015far\u0131 elde etmeden \u00f6nce 6 ba\u015far\u0131s\u0131zl\u0131k ya\u015fama olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu soruyu cevaplamak i\u00e7in negatif binom da\u011f\u0131l\u0131m\u0131n\u0131 a\u015fa\u011f\u0131daki parametrelerle kullanabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>k:<\/strong> ar\u0131za say\u0131s\u0131 = 6<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>r:<\/strong> ba\u015far\u0131 say\u0131s\u0131 = 4<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p:<\/strong> belirli bir denemede ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 = 0,5<\/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>P(X=6 ba\u015far\u0131s\u0131zl\u0131k)<\/strong> = <sub>6+4-1<\/sub> C <sub>6<\/sub> * (1-.5) <sup>4<\/sup> *(.5) <sup>6<\/sup> = (84)*(.0625)*(.015625) = <strong>0,08203<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Negatif binom da\u011f\u0131l\u0131m\u0131n\u0131n \u00f6zellikleri<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Negatif binom da\u011f\u0131l\u0131m\u0131 a\u015fa\u011f\u0131daki \u00f6zelliklere sahiptir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>R<\/em> ba\u015far\u0131 elde etmeden \u00f6nce bekledi\u011fimiz ortalama ba\u015far\u0131s\u0131zl\u0131k say\u0131s\u0131 <strong>pr\/(1-p)&#8217;<\/strong> dir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>r<\/em> ba\u015far\u0131y\u0131 elde etmeden \u00f6nce beklenen ba\u015far\u0131s\u0131zl\u0131k say\u0131s\u0131n\u0131n varyans\u0131 <strong>pr<\/strong> <strong>\/ (1-p) <sup>2&#8217;dir<\/sup><\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, yaz\u0131 tura att\u0131\u011f\u0131m\u0131z\u0131 ve &#8220;ba\u015far\u0131l\u0131&#8221; bir olay\u0131 tura gelmek olarak tan\u0131mlad\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">4 ba\u015far\u0131 elde etmeden \u00f6nce bekleyece\u011fimiz ortalama ba\u015far\u0131s\u0131zl\u0131k say\u0131s\u0131 (\u00f6rne\u011fin kuyruk ini\u015fi <strong>) pr\/(1-p)<\/strong> = (.5*4) \/ (1-.5) = <strong>4<\/strong> olacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">4 ba\u015far\u0131 elde etmeden \u00f6nce bekledi\u011fimiz ba\u015far\u0131s\u0131zl\u0131k say\u0131s\u0131n\u0131n varyans\u0131 <strong>pr\/(1-p) <sup>2<\/sup><\/strong> = (.5*4)\/(1-.5) <sup>2<\/sup> = <strong>8<\/strong> olacakt\u0131r.<\/span><\/p>\n<h3> <strong>Negatif Binom Da\u011f\u0131l\u0131m\u0131 Uygulama Problemleri<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Negatif binom da\u011f\u0131l\u0131m\u0131na 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\/negatif-binom-dagilim-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">negatif binom da\u011f\u0131l\u0131m hesaplay\u0131c\u0131s\u0131n\u0131<\/a> kullanaca\u011f\u0131z.<\/em><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Sorun 1<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Soru:<\/strong> Yaz\u0131 tura att\u0131\u011f\u0131m\u0131z\u0131 ve &#8220;ba\u015far\u0131l\u0131&#8221; bir olay\u0131 yaz\u0131 tura atmak olarak tan\u0131mlad\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m. Toplam 4 ba\u015far\u0131 ya\u015famadan \u00f6nce 3 ba\u015far\u0131s\u0131zl\u0131k ya\u015fama olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\"><strong>Cevap:<\/strong> k = 3 ba\u015far\u0131s\u0131zl\u0131k, r = 4 ba\u015far\u0131 ve p = 0,5 olan negatif binom da\u011f\u0131l\u0131m hesaplay\u0131c\u0131s\u0131n\u0131 kullanarak P(X=3) = <strong>0,15625&#8217;i<\/strong> buluruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Sorun 2<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Soru:<\/strong> Kap\u0131 kap\u0131 dola\u015f\u0131p \u015feker satt\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m. Birisi \u015feker sat\u0131n al\u0131rsa bunu &#8220;ba\u015far\u0131&#8221; olarak kabul ederiz. Belirli bir ki\u015finin \u015feker alma olas\u0131l\u0131\u011f\u0131 0,4&#8217;t\u00fcr. Toplam 5 ba\u015far\u0131 elde etmeden \u00f6nce 8 ba\u015far\u0131s\u0131zl\u0131k ya\u015fama olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\"><strong>Cevap:<\/strong> k = 8 ba\u015far\u0131s\u0131zl\u0131k, r = 5 ba\u015far\u0131 ve p = 0,4 olan negatif binom da\u011f\u0131l\u0131m hesaplay\u0131c\u0131s\u0131n\u0131 kullanarak P(X=8) = <strong>0,08514<\/strong> oldu\u011funu buluruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Sorun 3<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Soru:<\/strong> Diyelim ki bir zar at\u0131yoruz ve &#8220;ba\u015far\u0131l\u0131&#8221; bir at\u0131\u015f\u0131n 5 say\u0131s\u0131na gelmesi olarak tan\u0131ml\u0131yoruz. Belirli bir at\u0131\u015fta zar\u0131n 5&#8217;e gelme olas\u0131l\u0131\u011f\u0131 1\/6 = 0,167&#8217;dir. Toplam 3 ba\u015far\u0131 ya\u015famadan \u00f6nce 4 ba\u015far\u0131s\u0131zl\u0131k ya\u015fama olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\"><strong>Cevap:<\/strong> k = 4 ba\u015far\u0131s\u0131zl\u0131k, r = 3 ba\u015far\u0131 ve p = 0,167 ile negatif binom da\u011f\u0131l\u0131m hesaplay\u0131c\u0131s\u0131n\u0131 kullanarak P(X=4) = <strong>0,03364&#8217;\u00fc<\/strong> buluruz.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Negatif binom da\u011f\u0131l\u0131m\u0131, bir dizi Bernoulli denemesinde belirli say\u0131da ba\u015far\u0131 elde edilmeden \u00f6nce belirli say\u0131da ba\u015far\u0131s\u0131zl\u0131\u011f\u0131n ya\u015fanma olas\u0131l\u0131\u011f\u0131n\u0131 tan\u0131mlar. Bir Bernoulli denemesi yaln\u0131zca iki olas\u0131 sonucu olan bir deneydir \u2013 \u201cba\u015far\u0131l\u0131\u201d veya \u201cba\u015far\u0131s\u0131z\u201d ve ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 deney her yap\u0131ld\u0131\u011f\u0131nda ayn\u0131d\u0131r. Bernoulli makalesinin bir \u00f6rne\u011fi yaz\u0131 tura atmakt\u0131r. Para yaln\u0131zca iki tura gelebilir (turalara &#8220;vuru\u015f&#8221;, yaz\u0131lara [&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-768","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>Negatif Binom Da\u011f\u0131l\u0131m\u0131&#039;na Giri\u015f - Statorials<\/title>\n<meta name=\"description\" content=\"Resmi bir tan\u0131m ve birka\u00e7 \u00f6rnek i\u00e7eren, negatif binom da\u011f\u0131l\u0131m\u0131na 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\/negatif-binom-dagilimi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Negatif Binom Da\u011f\u0131l\u0131m\u0131&#039;na Giri\u015f - Statorials\" \/>\n<meta property=\"og:description\" content=\"Resmi bir tan\u0131m ve birka\u00e7 \u00f6rnek i\u00e7eren, negatif binom da\u011f\u0131l\u0131m\u0131na basit bir giri\u015f.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/negatif-binom-dagilimi\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-28T20:06:46+00:00\" \/>\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=\"3 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/negatif-binom-dagilimi\/\",\"url\":\"https:\/\/statorials.org\/tr\/negatif-binom-dagilimi\/\",\"name\":\"Negatif Binom Da\u011f\u0131l\u0131m\u0131&#39;na Giri\u015f - Statorials\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-07-28T20:06:46+00:00\",\"dateModified\":\"2023-07-28T20:06:46+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Resmi bir tan\u0131m ve birka\u00e7 \u00f6rnek i\u00e7eren, negatif binom da\u011f\u0131l\u0131m\u0131na basit bir giri\u015f.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/negatif-binom-dagilimi\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/negatif-binom-dagilimi\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/negatif-binom-dagilimi\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Negatif binom da\u011f\u0131l\u0131m\u0131na 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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