{"id":937,"date":"2023-07-28T06:28:19","date_gmt":"2023-07-28T06:28:19","guid":{"rendered":"https:\/\/statorials.org\/tr\/binom-dagilim-formu\/"},"modified":"2023-07-28T06:28:19","modified_gmt":"2023-07-28T06:28:19","slug":"binom-dagilim-formu","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/binom-dagilim-formu\/","title":{"rendered":"Binom da\u011f\u0131l\u0131m\u0131n\u0131n \u015feklini anlama"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/binom-dagilimi-1\/\" target=\"_blank\" rel=\"noopener noreferrer\">Binom da\u011f\u0131l\u0131m\u0131,<\/a> <em>n<\/em> binom deneyinde <em>k<\/em> ba\u015far\u0131 elde etme olas\u0131l\u0131\u011f\u0131n\u0131 tan\u0131mlar.<\/span><\/p>\n<p> <span style=\"color: #000000;\">E\u011fer bir<\/span> X <a href=\"https:\/\/statorials.org\/tr\/rastgele-degiskenler\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"random variable (opens in a new tab)\">rastgele de\u011fi\u015fkeni<\/a> <span style=\"color: #000000;\"><em>binom<\/em> da\u011f\u0131l\u0131m\u0131n\u0131 takip ediyorsa, <em>X<\/em> = <em>k<\/em> ba\u015far\u0131s\u0131n\u0131n olas\u0131l\u0131\u011f\u0131 a\u015fa\u011f\u0131daki form\u00fclle bulunabilir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=k) = <sub>n<\/sub> C <sub>k<\/sub> * p <sup>k<\/sup> * (1-p) <sup>nk<\/sup><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> deneme say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>k:<\/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>n<\/sub> C <sub>k<\/sub> :<\/strong> <em>n<\/em> denemede <em>k<\/em> ba\u015far\u0131 elde etmenin yollar\u0131n\u0131n say\u0131s\u0131<\/span><\/li>\n<\/ul>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki iki durumdan bir veya daha fazlas\u0131 meydana geldi\u011finde binom olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 \u00e7an \u015feklinde olma e\u011filimindedir:<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\"><strong>1.<\/strong> \u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc (n) b\u00fcy\u00fckt\u00fcr.<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\"><strong>2.<\/strong> Belirli bir denemenin ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 (p) 0,5&#8217;e yak\u0131nd\u0131r.<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\">Bununla birlikte, bu ko\u015fullar\u0131n hi\u00e7biri meydana gelmedi\u011finde binom olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 \u00e7arp\u0131k olma e\u011filimindedir.<\/span> <span style=\"color: #000000;\">Bunu a\u00e7\u0131klamak i\u00e7in a\u015fa\u011f\u0131daki \u00f6rnekleri g\u00f6z \u00f6n\u00fcnde bulundurun:<\/span><\/p>\n<h3 data-slot-rendered-dynamic=\"true\"> <strong>\u00d6rnek 1: \u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc (n) b\u00fcy\u00fck<\/strong><\/h3>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki grafik n = <strong>200<\/strong> ve p = <strong>0,5<\/strong> durumundaki olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6stermektedir.<\/span> <\/p>\n<p data-slot-rendered-dynamic=\"true\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9924 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/binomialshape1.png\" alt=\"Binom da\u011f\u0131l\u0131m formu\" width=\"457\" height=\"439\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\">X ekseni 200 denemedeki ba\u015far\u0131 say\u0131s\u0131n\u0131, y ekseni ise bu say\u0131daki ba\u015far\u0131n\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\"><strong>(1)<\/strong> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc b\u00fcy\u00fck oldu\u011fundan ve <strong>(2)<\/strong> belirli bir deneme i\u00e7in ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 0,5&#8217;e yak\u0131n oldu\u011fundan olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 \u00e7an \u015feklindedir.<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\">Belirli bir deneme i\u00e7in ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 (p) 0,5&#8217;e yak\u0131n olmasa bile, \u00f6rneklem boyutu (n) b\u00fcy\u00fck oldu\u011fu s\u00fcrece olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 \u00e7an \u015feklinde kalacakt\u0131r. Bunu g\u00f6stermek i\u00e7in, p = 0,2 ve p = 0,8 oldu\u011funda a\u015fa\u011f\u0131daki iki senaryoyu g\u00f6z \u00f6n\u00fcnde bulundurun.<\/span> <\/p>\n<p data-slot-rendered-dynamic=\"true\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9925 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/binomeforme2.png\" alt=\"\" width=\"457\" height=\"438\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p data-slot-rendered-dynamic=\"true\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9926 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/binomeforme3.png\" alt=\"\" width=\"457\" height=\"438\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\">Her iki senaryoda da olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n nas\u0131l \u00e7an \u015feklinde oldu\u011funa dikkat edin.<\/span><\/p>\n<h3 data-slot-rendered-dynamic=\"true\"> <strong>\u00d6rnek 2: Ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 (p) 0,5&#8217;e yak\u0131nd\u0131r<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki grafik n = <strong>10<\/strong> ve p = <strong>0,4<\/strong> durumundaki olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6stermektedir.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9927 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/binomeforme4.png\" alt=\"P = 0,5 oldu\u011funda binom da\u011f\u0131l\u0131m formu\" width=\"384\" height=\"371\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc (n = 10) k\u00fc\u00e7\u00fck olmas\u0131na ra\u011fmen, belirli bir denemenin ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 (p = 0,4) 0,5&#8217;e yak\u0131n oldu\u011fundan olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 \u00e7an \u015feklinde kal\u0131r.<\/span><\/p>\n<h3 data-slot-rendered-dynamic=\"true\"> <strong>\u00d6rnek 3: \u00c7arp\u0131k binom da\u011f\u0131l\u0131mlar\u0131<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Ne <strong>(1)<\/strong> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc b\u00fcy\u00fck oldu\u011funda ne de <strong>(2)<\/strong> belirli bir denemenin ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 0,5&#8217;e yak\u0131n oldu\u011funda, binom olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 sola veya sa\u011fa \u00e7arp\u0131k olacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin a\u015fa\u011f\u0131daki grafik n = <strong>20<\/strong> ve p = <strong>0,1<\/strong> oldu\u011funda olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6stermektedir.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9928 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/binomeforme5.png\" alt=\"Asimetrik binom da\u011f\u0131l\u0131m\u0131\" width=\"407\" height=\"387\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Da\u011f\u0131t\u0131m\u0131n nas\u0131l sa\u011fa \u00e7arp\u0131k oldu\u011funa dikkat edin.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki grafik ise n = <strong>20<\/strong> ve p = <strong>0,9<\/strong> durumundaki olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6stermektedir.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9929 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/binomeforme6.png\" alt=\"Sola \u00e7arp\u0131k binom da\u011f\u0131l\u0131m\u0131\" width=\"406\" height=\"402\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Da\u011f\u0131t\u0131m\u0131n nas\u0131l sola \u00e7arp\u0131k oldu\u011funa dikkat edin.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Son notlar<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bu makaledeki grafiklerin her biri R istatistiksel programlama dili kullan\u0131larak olu\u015fturulmu\u015ftur. <a href=\"https:\/\/statorials.org\/tr\/binom-dagilimini-cizin-r\/\" target=\"_blank\" rel=\"noopener noreferrer\">Bu \u00f6\u011freticiyi<\/a> kullanarak R&#8217;de kendi binom olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131n\u0131z\u0131 nas\u0131l \u00e7izece\u011finizi \u00f6\u011frenin.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Binom da\u011f\u0131l\u0131m\u0131, n binom deneyinde k ba\u015far\u0131 elde etme olas\u0131l\u0131\u011f\u0131n\u0131 tan\u0131mlar. E\u011fer bir X rastgele de\u011fi\u015fkeni binom da\u011f\u0131l\u0131m\u0131n\u0131 takip ediyorsa, X = k ba\u015far\u0131s\u0131n\u0131n olas\u0131l\u0131\u011f\u0131 a\u015fa\u011f\u0131daki form\u00fclle bulunabilir: P(X=k) = n C k * p k * (1-p) nk Alt\u0131n: n: deneme say\u0131s\u0131 k: ba\u015far\u0131 say\u0131s\u0131 p: belirli bir denemede ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 n C k [&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-937","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>Binom da\u011f\u0131l\u0131m\u0131n\u0131n \u015feklini anlama - Statorials<\/title>\n<meta name=\"description\" content=\"Binom da\u011f\u0131l\u0131m\u0131n\u0131n \u015feklinin nas\u0131l anla\u015f\u0131laca\u011f\u0131na ve yorumlanaca\u011f\u0131na dair basit bir a\u00e7\u0131klama.\" \/>\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\/binom-dagilim-formu\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Binom da\u011f\u0131l\u0131m\u0131n\u0131n \u015feklini anlama - 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