{"id":763,"date":"2023-07-28T20:30:47","date_gmt":"2023-07-28T20:30:47","guid":{"rendered":"https:\/\/statorials.org\/tr\/geometrik-dagilim\/"},"modified":"2023-07-28T20:30:47","modified_gmt":"2023-07-28T20:30:47","slug":"geometrik-dagilim","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/geometrik-dagilim\/","title":{"rendered":"Geometrik da\u011f\u0131l\u0131ma giri\u015f"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Geometrik da\u011f\u0131l\u0131m,<\/strong> bir dizi Bernoulli denemesinde ilk ba\u015far\u0131y\u0131 elde etmeden \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;\">E\u011fer bir <em>X<\/em> <a href=\"https:\/\/statorials.org\/tr\/rastgele-degiskenler\/\" target=\"_blank\" rel=\"noopener\">rastgele de\u011fi\u015fkeni<\/a> geometrik bir da\u011f\u0131l\u0131m izliyorsa, ilk ba\u015far\u0131y\u0131 elde etmeden \u00f6nce <em>k tane<\/em> ba\u015far\u0131s\u0131zl\u0131\u011f\u0131n ya\u015fanma olas\u0131l\u0131\u011f\u0131 a\u015fa\u011f\u0131daki form\u00fclle bulunabilir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=k) = (1-p) <sup>kp<\/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> ilk ba\u015far\u0131dan \u00f6nceki ba\u015far\u0131s\u0131zl\u0131k say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p:<\/strong> her denemede ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, adil bir yaz\u0131 tura gelene kadar ka\u00e7 kez atmam\u0131z gerekti\u011fini bilmek istedi\u011fimizi varsayal\u0131m. 0, 1, 2, 3 ar\u0131za vb. ya\u015fanma olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in yukar\u0131daki form\u00fcl\u00fc kullanabiliriz. para tura gelmeden \u00f6nce:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em><strong>Not:<\/strong> Madeni para ilk at\u0131\u015fta tura gelirse 0 &#8220;ba\u015far\u0131s\u0131zl\u0131k&#8221; ya\u015fayabilir.<\/em><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=0)<\/strong> = (1-.5) <sup>0<\/sup> (.5) = <strong>0.5<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=1)<\/strong> = (1-.5) <sup>1<\/sup> (.5) = <strong>0.25<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=2)<\/strong> = (1-.5) <sup>2<\/sup> (.5) = <strong>0.125<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=3)<\/strong> = (1-0,5) <sup>3<\/sup> (0,5) = <strong>0,0625<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Herhangi bir say\u0131da yaz\u0131 tura atma olas\u0131l\u0131\u011f\u0131n\u0131 sonsuza kadar hesaplayabiliriz. Daha sonra bu olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6rselle\u015ftirmek i\u00e7in basit bir histogram olu\u015fturuyoruz:<\/span> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8160 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/geomdist1.png\" alt=\"Geometrik olas\u0131l\u0131k da\u011f\u0131l\u0131m histogram\u0131\" width=\"442\" height=\"313\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h3> <strong>K\u00fcm\u00fclatif geometrik olas\u0131l\u0131klar\u0131n hesaplanmas\u0131<\/strong><\/h3>\n<p> \u0130lk ba\u015far\u0131ya ula\u015fana kadar k veya daha az ba\u015far\u0131s\u0131zl\u0131k ya\u015famam\u0131z\u0131n k\u00fcm\u00fclatif olas\u0131l\u0131\u011f\u0131 <span style=\"color: #000000;\">a\u015fa\u011f\u0131daki form\u00fclle<\/span> <span style=\"color: #000000;\"><em>bulunabilir<\/em> <strong>:<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X\u2264k) = 1 \u2013 (1-p) <sup>k+1<\/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> ilk ba\u015far\u0131dan \u00f6nceki ba\u015far\u0131s\u0131zl\u0131k say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p:<\/strong> her denemede ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, madeni paran\u0131n nihayet tura gelmesinden \u00f6nce \u00fc\u00e7 veya daha az &#8220;\u0131skalama&#8221;n\u0131n gerekli olma olas\u0131l\u0131\u011f\u0131n\u0131 bilmek istedi\u011fimizi varsayal\u0131m. Bu olas\u0131l\u0131\u011f\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullan\u0131r\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X\u22643)<\/strong> = 1 \u2013 (1-0,5) <sup>3+1<\/sup> = <strong>0,9375<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Her k\u00fcm\u00fclatif olas\u0131l\u0131\u011f\u0131 benzer bir form\u00fcl kullanarak hesaplayabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X\u22640)<\/strong> = 1 \u2013 (1-.5) <sup>0+1<\/sup> = <strong>0.5<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X\u22641)<\/strong> = 1 \u2013 (1-0,5) <sup>1+1<\/sup> = <strong>0,75<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X\u22642)<\/strong> = 1 \u2013 (1-0,5) <sup>2+1<\/sup> = <strong>0,875<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu k\u00fcm\u00fclatif olas\u0131l\u0131klar\u0131, herhangi bir say\u0131daki yaz\u0131-tura at\u0131\u015flar\u0131 i\u00e7in sonsuza kadar hesaplayabiliriz. Daha sonra bu k\u00fcm\u00fclatif olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6rselle\u015ftirmek i\u00e7in bir histogram olu\u015fturabiliriz:<\/span> <\/p>\n<div class=\"wp-block-image\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8162 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/geomdist2.png\" alt=\"Geometrik k\u00fcm\u00fclatif olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131\" width=\"459\" height=\"283\" srcset=\"\" sizes=\"auto, \"><\/div>\n<h3> <strong>Geometrik da\u011f\u0131l\u0131m\u0131n \u00f6zellikleri<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Geometrik da\u011f\u0131l\u0131m a\u015fa\u011f\u0131daki \u00f6zelliklere sahiptir:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Da\u011f\u0131l\u0131m\u0131n ortalamas\u0131 <strong>(1-p) \/ p&#8217;dir<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Da\u011f\u0131l\u0131m\u0131n varyans\u0131 <strong>(1-p) \/ p <sup>2&#8217;dir<\/sup><\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir madalyonun yaz\u0131 gelmeden \u00f6nce tura gelmesini bekledi\u011fimiz ortalama say\u0131 (1-p) \/ p = (1-.5) \/ .5 = <strong>1<\/strong> olacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Tura gelene kadar at\u0131\u015f say\u0131s\u0131n\u0131n varyans\u0131 (1-p)\/ <sup>p2<\/sup> =(1-.5)\/ olacakt\u0131r. <sup>52<\/sup> = <strong>2<\/strong> .<\/span><\/p>\n<h3> <strong>Geometrik Da\u011f\u0131l\u0131m Uygulama Problemleri<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Geometrik da\u011f\u0131l\u0131m 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\/geometrik-dagilim-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">Geometrik Da\u011f\u0131l\u0131m Hesaplay\u0131c\u0131y\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> Bir ara\u015ft\u0131rmac\u0131, insanlara belirli bir yasay\u0131 destekleyip desteklemediklerini sormak i\u00e7in k\u00fct\u00fcphanenin \u00f6n\u00fcnde bekliyor. Belirli bir ki\u015finin yasay\u0131 destekleme olas\u0131l\u0131\u011f\u0131 p = 0,2&#8217;dir. Ara\u015ft\u0131rmac\u0131n\u0131n konu\u015ftu\u011fu d\u00f6rd\u00fcnc\u00fc ki\u015finin yasay\u0131 ilk destekleyen ki\u015fi olma olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\"><strong>Cevap:<\/strong> \u0130lk ba\u015far\u0131ya kadar \u201cba\u015far\u0131s\u0131zl\u0131k\u201d say\u0131s\u0131, yani ilk ki\u015fi destekleyene kadar kanunu desteklemeyenlerin say\u0131s\u0131 3&#8217;t\u00fcr. Yani p = 0,2 ve x olan geometrik da\u011f\u0131l\u0131m hesaplay\u0131c\u0131s\u0131 kullan\u0131ld\u0131\u011f\u0131nda = 3 ba\u015far\u0131s\u0131zl\u0131k, P(X=3) = <strong>0,10240<\/strong> oldu\u011funu buluruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Sorun 2<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Soru:<\/strong> Bir ara\u015ft\u0131rmac\u0131, insanlara belirli bir yasay\u0131 destekleyip desteklemediklerini sormak i\u00e7in k\u00fct\u00fcphanenin \u00f6n\u00fcnde bekliyor. Belirli bir ki\u015finin yasay\u0131 destekleme olas\u0131l\u0131\u011f\u0131 p = 0,2&#8217;dir. Ara\u015ft\u0131rmac\u0131n\u0131n yasay\u0131 destekleyen birini bulmak i\u00e7in d\u00f6rtten <em>fazla<\/em> ki\u015fiyle konu\u015fmak zorunda kalmas\u0131 olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\"><strong>Cevap:<\/strong> P =0,2 ve x = 4 hatal\u0131 geometrik da\u011f\u0131l\u0131m hesaplay\u0131c\u0131s\u0131n\u0131 kullanarak P(X&gt;4) = <strong>0,32768&#8217;i<\/strong> buluruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Sorun 3<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Soru:<\/strong> Bir ara\u015ft\u0131rmac\u0131, insanlara belirli bir yasay\u0131 destekleyip desteklemediklerini sormak i\u00e7in k\u00fct\u00fcphanenin \u00f6n\u00fcnde bekliyor. Belirli bir ki\u015finin yasay\u0131 destekleme olas\u0131l\u0131\u011f\u0131 p = 0,2&#8217;dir. Ara\u015ft\u0131rmac\u0131n\u0131n yasay\u0131 destekleyen birini bulana kadar konu\u015fmas\u0131 gereken tahmini ki\u015fi say\u0131s\u0131 nedir?<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\"><strong>Cevap:<\/strong> Geometrik da\u011f\u0131l\u0131m\u0131n ortalamas\u0131n\u0131n <strong>(1-p) \/ p<\/strong> oldu\u011funu hat\u0131rlay\u0131n. Bu durumda ortalama (1-.2) \/ .2 = <strong>4<\/strong> olacakt\u0131r.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Geometrik da\u011f\u0131l\u0131m, bir dizi Bernoulli denemesinde ilk ba\u015far\u0131y\u0131 elde etmeden \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 ise &#8220;ba\u015far\u0131s\u0131zl\u0131k&#8221; [&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-763","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>Geometrik Da\u011f\u0131l\u0131ma Giri\u015f - Statoryaller<\/title>\n<meta name=\"description\" content=\"Birka\u00e7 ad\u0131m ad\u0131m \u00f6rnek i\u00e7eren, geometrik 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\/geometrik-dagilim\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Geometrik Da\u011f\u0131l\u0131ma Giri\u015f - Statoryaller\" \/>\n<meta property=\"og:description\" content=\"Birka\u00e7 ad\u0131m ad\u0131m \u00f6rnek i\u00e7eren, geometrik da\u011f\u0131l\u0131ma basit bir giri\u015f.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/geometrik-dagilim\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-28T20:30:47+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/geomdist1.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=\"4 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/geometrik-dagilim\/\",\"url\":\"https:\/\/statorials.org\/tr\/geometrik-dagilim\/\",\"name\":\"Geometrik Da\u011f\u0131l\u0131ma Giri\u015f - Statoryaller\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-07-28T20:30:47+00:00\",\"dateModified\":\"2023-07-28T20:30:47+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Birka\u00e7 ad\u0131m ad\u0131m \u00f6rnek i\u00e7eren, geometrik da\u011f\u0131l\u0131ma basit bir giri\u015f.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/geometrik-dagilim\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/geometrik-dagilim\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/geometrik-dagilim\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Geometrik da\u011f\u0131l\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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