{"id":1424,"date":"2023-07-26T10:59:27","date_gmt":"2023-07-26T10:59:27","guid":{"rendered":"https:\/\/statorials.org\/tr\/kosullu-dagitim\/"},"modified":"2023-07-26T10:59:27","modified_gmt":"2023-07-26T10:59:27","slug":"kosullu-dagitim","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/kosullu-dagitim\/","title":{"rendered":"I\u0307statistikte ko\u015fullu da\u011f\u0131l\u0131m nedir?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><em>X<\/em> ve <em>Y<\/em> ortakla\u015fa da\u011f\u0131t\u0131lan iki <a href=\"https:\/\/statorials.org\/tr\/rastgele-degiskenler\/\" target=\"_blank\" rel=\"noopener\">rastgele de\u011fi\u015fkense<\/a> , o zaman <em>X&#8217;in<\/em> verildi\u011fi <em>Y&#8217;nin<\/em> <strong>ko\u015fullu da\u011f\u0131l\u0131m\u0131,<\/strong> <em>X&#8217;in<\/em> belirli bir de\u011fer oldu\u011fu bilindi\u011finde <em>Y&#8217;nin<\/em> olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, a\u015fa\u011f\u0131daki iki y\u00f6nl\u00fc tablo 100 ki\u015fiye hangi sporu tercih ettiklerini soran bir anketin sonu\u00e7lar\u0131n\u0131 g\u00f6stermektedir: beyzbol, basketbol veya futbol.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12767 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/marginal1.png\" alt=\"\" width=\"357\" height=\"142\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bir ki\u015finin erkek oldu\u011fu <em>g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda<\/em> belirli bir sporu tercih etme olas\u0131l\u0131\u011f\u0131n\u0131 bilmek istiyorsak, bu bir ko\u015fullu da\u011f\u0131l\u0131m \u00f6rne\u011fidir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir rastgele de\u011fi\u015fkenin de\u011feri biliniyor (ki\u015fi bir erkek), ancak di\u011fer rastgele de\u011fi\u015fkenin de\u011feri bilinmiyor (en sevdi\u011fi sporu bilmiyoruz).<\/span><\/p>\n<p> <span style=\"color: #000000;\">Erkekler aras\u0131ndaki spor tercihlerinin ko\u015fullu da\u011f\u0131l\u0131m\u0131n\u0131 bulmak i\u00e7in tablodaki <strong>erkeklere<\/strong> y\u00f6nelik \u00e7izginin de\u011ferlerine bakmam\u0131z yeterlidir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14072 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/conditionnelledist1.png\" alt=\"Ko\u015fullu Da\u011f\u0131t\u0131m \u00d6rne\u011fi\" width=\"366\" height=\"158\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Ko\u015fullu da\u011f\u0131l\u0131m \u015fu \u015fekilde hesaplanacakt\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Beyzbolu tercih eden erkekler: 13\/48 = <strong>0,2708<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">Basketbolu tercih eden erkekler: 15\/48 = <strong>0,3125<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">Futbolu tercih eden erkekler: 20\/48 = <strong>0,4167<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Olas\u0131l\u0131klar\u0131n toplam\u0131n\u0131n 1 oldu\u011funa dikkat edin: 13\/48 + 15\/48 + 20\/48 = 48\/48 = 1.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu ko\u015fullu da\u011f\u0131l\u0131m\u0131 \u015fu t\u00fcr sorular\u0131 yan\u0131tlamak i\u00e7in kullanabiliriz: <em>Bir bireyin erkek oldu\u011fu g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda, beyzbolun onun en sevdi\u011fi spor olma olas\u0131l\u0131\u011f\u0131 nedir?<\/em><\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha \u00f6nce hesaplad\u0131\u011f\u0131m\u0131z ko\u015fullu da\u011f\u0131l\u0131mdan olas\u0131l\u0131\u011f\u0131n <strong>0,2708<\/strong> oldu\u011funu g\u00f6rebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Teknik a\u00e7\u0131dan, ko\u015fullu bir da\u011f\u0131l\u0131m hesaplad\u0131\u011f\u0131m\u0131zda, genel n\u00fcfusun belirli bir <strong>alt pop\u00fclasyonuyla<\/strong> ilgilendi\u011fimizi s\u00f6yleriz. \u00d6nceki \u00f6rnekteki alt pop\u00fclasyon erkeklerden olu\u015fuyordu:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14073 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/conditionnelledist2.png\" alt=\"Ko\u015fullu bir da\u011f\u0131l\u0131m i\u00e7in alt pop\u00fclasyon\" width=\"449\" height=\"145\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Ve bu alt pop\u00fclasyona ba\u011fl\u0131 bir olas\u0131l\u0131\u011f\u0131 hesaplamak istedi\u011fimizde, belirli bir <strong>ilgi \u00e7ekici karakterle<\/strong> ilgilendi\u011fimizi s\u00f6yleriz. \u00d6nceki \u00f6rnekteki ilgin\u00e7 karakter beyzboldu:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14074 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/conditionnelledist3.png\" alt=\"\u0130statistiklerde ko\u015fullu da\u011f\u0131l\u0131m\" width=\"457\" height=\"198\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u0130lgilenilen \u00f6zelli\u011fin alt pop\u00fclasyonda ortaya \u00e7\u0131kma olas\u0131l\u0131\u011f\u0131n\u0131 bulmak i\u00e7in, ilgilenilen \u00f6zelli\u011fin de\u011ferini (\u00f6rn. 13) alt pop\u00fclasyonun toplam de\u011ferlerine (\u00f6rn. 48) b\u00f6lerek 13\/48 = <strong>0,2708<\/strong> elde ederiz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ko\u015fullu da\u011f\u0131l\u0131mlar ve ba\u011f\u0131ms\u0131zl\u0131k<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Rastgele de\u011fi\u015fkenler <em>X<\/em> ve <em>Y&#8217;nin<\/em> ba\u011f\u0131ms\u0131z oldu\u011funu ancak ve ancak <em>X&#8217;in<\/em> verildi\u011fi <em>Y&#8217;nin<\/em> ko\u015fullu da\u011f\u0131l\u0131m\u0131n\u0131n, <em>X&#8217;in<\/em> t\u00fcm olas\u0131 ger\u00e7ekle\u015fmeleri i\u00e7in <em>Y&#8217;nin<\/em> ko\u015fulsuz da\u011f\u0131l\u0131m\u0131na e\u015fit olmas\u0131 durumunda s\u00f6yleyebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin bir \u00f6nceki tabloda \u201cbeyzbolu tercih ediyor\u201d ve \u201cerkek\u201d testlerinin ba\u011f\u0131ms\u0131z oldu\u011funu g\u00f6rebiliyor muyuz?<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu soruyu cevaplamak i\u00e7in a\u015fa\u011f\u0131daki olas\u0131l\u0131klar\u0131 hesaplayal\u0131m:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">P(beyzbolu tercih eder)<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(beyzbolu tercih ediyor | erkek) \u201cerkek olduklar\u0131 g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda beyzbolu tercih ediyor<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Belirli bir bireyin beyzbolu tercih etme olas\u0131l\u0131\u011f\u0131:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">P (beyzbolu tercih ediyor) = 36\/100 = <strong>0,36<\/strong> .<\/span> <\/li>\n<\/ul>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14075 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/conditionnelledist4.png\" alt=\"\" width=\"361\" height=\"153\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Belirli bir ki\u015finin erkek oldu\u011fu g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda beyzbolu tercih etme olas\u0131l\u0131\u011f\u0131<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">P (beyzbolu tercih ediyor | erkek) = 13\/48 = <strong>0,2708<\/strong> .<\/span> <\/li>\n<\/ul>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14076 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/conditionnelledist5.png\" alt=\"\" width=\"360\" height=\"151\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">P(beyzbolu tercih ediyor) P(beyzbolu tercih ediyor | erkek) e\u015fit olmad\u0131\u011f\u0131ndan, spor tercihi ve cinsiyetin rastgele de\u011fi\u015fkenleri ba\u011f\u0131ms\u0131z <em>de\u011fildir<\/em> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ko\u015fullu da\u011f\u0131l\u0131mlar\u0131 neden kullanmal\u0131s\u0131n\u0131z?<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Ko\u015fullu olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131 faydal\u0131d\u0131r \u00e7\u00fcnk\u00fc s\u0131kl\u0131kla iki de\u011fi\u015fken (cinsiyet ve spor tercihleri gibi) i\u00e7in veri topluyoruz, ancak de\u011fi\u015fkenlerden birinin de\u011ferini <em>bildi\u011fimizde<\/em> olas\u0131l\u0131k hakk\u0131ndaki sorular\u0131 yan\u0131tlamak istiyoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6nceki \u00f6rnekte, belirli bir bireyin erkek oldu\u011funu bildi\u011fimiz ve bu bireyin beyzbolu tercih etme olas\u0131l\u0131\u011f\u0131n\u0131 bilmek istedi\u011fimiz senaryoyu de\u011ferlendirdik.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ger\u00e7ek hayatta bir de\u011fi\u015fkenin de\u011ferini bildi\u011fimiz ve ba\u015fka bir de\u011fi\u015fkenin belirli bir de\u011feri alma olas\u0131l\u0131\u011f\u0131n\u0131 bulmak i\u00e7in ko\u015fullu da\u011f\u0131l\u0131m kullanabilece\u011fimiz bir\u00e7ok durum vard\u0131r.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/tr\/marjinal-dagilim\/\" target=\"_blank\" rel=\"noopener\">Marjinal da\u011f\u0131l\u0131m nedir?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/ortak-olasilik-dagilimi\/\" target=\"_blank\" rel=\"noopener\">Ortak olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 nedir?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/cift-yonlu-kosullu-bagil-frekans-tablosu\/\" target=\"_blank\" rel=\"noopener\">\u00c7ift giri\u015fli bir tabloda ko\u015fullu ba\u011f\u0131l frekans nas\u0131l bulunur?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>X ve Y ortakla\u015fa da\u011f\u0131t\u0131lan iki rastgele de\u011fi\u015fkense , o zaman X&#8217;in verildi\u011fi Y&#8217;nin ko\u015fullu da\u011f\u0131l\u0131m\u0131, X&#8217;in belirli bir de\u011fer oldu\u011fu bilindi\u011finde Y&#8217;nin olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r. \u00d6rne\u011fin, a\u015fa\u011f\u0131daki iki y\u00f6nl\u00fc tablo 100 ki\u015fiye hangi sporu tercih ettiklerini soran bir anketin sonu\u00e7lar\u0131n\u0131 g\u00f6stermektedir: beyzbol, basketbol veya futbol. Bir ki\u015finin erkek oldu\u011fu g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda belirli bir sporu [&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-1424","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>\u0130statistikte ko\u015fullu da\u011f\u0131l\u0131m nedir?<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, bir tan\u0131m ve \u00e7e\u015fitli \u00f6rnekler de dahil olmak \u00fczere ko\u015fullu da\u011f\u0131t\u0131m\u0131n bir a\u00e7\u0131klamas\u0131 sa\u011flanmaktad\u0131r.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link 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