{"id":1614,"date":"2023-07-25T15:56:40","date_gmt":"2023-07-25T15:56:40","guid":{"rendered":"https:\/\/statorials.org\/tr\/geometrik-dagilim-gercek-ornekleri\/"},"modified":"2023-07-25T15:56:40","modified_gmt":"2023-07-25T15:56:40","slug":"geometrik-dagilim-gercek-ornekleri","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/geometrik-dagilim-gercek-ornekleri\/","title":{"rendered":"Geometrik da\u011f\u0131l\u0131ma 5 somut \u00f6rnek"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/geometrik-dagilim\/\" target=\"_blank\" rel=\"noopener\">Geometrik da\u011f\u0131l\u0131m,<\/a> 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 modellemek i\u00e7in kullan\u0131lan bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r.<\/span><\/p>\n<blockquote>\n<p> <span style=\"color: #000000;\"><strong>Bernoulli denemesi<\/strong> yaln\u0131zca iki olas\u0131 sonucu olan bir deneydir: \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;\">Bu yaz\u0131m\u0131zda ger\u00e7ek d\u00fcnyada geometrik da\u011f\u0131l\u0131m\u0131n kullan\u0131m\u0131na ili\u015fkin 5 \u00f6rne\u011fi payla\u015f\u0131yoruz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 1: K\u00f6\u015fe at\u0131\u015flar\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Farz edelim ki, adil bir yaz\u0131 tura gelene kadar ka\u00e7 kez atmam\u0131z gerekti\u011fini bilmek istiyoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">0, 1, 2, 3 ar\u0131za vb. ya\u015fanma olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in a\u015fa\u011f\u0131daki form\u00fclleri 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<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 2: Bir yasay\u0131 destekleyenler<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir ara\u015ft\u0131rmac\u0131n\u0131n k\u00fct\u00fcphanenin \u00f6n\u00fcnde bekledi\u011fini ve insanlara belirli bir yasay\u0131 destekleyip desteklemediklerini sordu\u011funu varsayal\u0131m. Belirli bir ki\u015finin yasay\u0131 destekleme olas\u0131l\u0131\u011f\u0131 p = 0,2&#8217;dir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">0, 1, 2 ki\u015fi vb. ki\u015filerle g\u00f6r\u00fc\u015fme olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in a\u015fa\u011f\u0131daki form\u00fclleri kullanabiliriz. ara\u015ft\u0131rmac\u0131 yasay\u0131 destekleyen biriyle konu\u015fmadan \u00f6nce:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=0)<\/strong> = (1-.2) <sup>0<\/sup> (.2) = <strong>0.2<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=1)<\/strong> = (1-.2) <sup>1<\/sup> (.2) = <strong>0.16<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=2)<\/strong> = (1-.2) <sup>2<\/sup> (.2) = <strong>0.128<\/strong><\/span><\/p>\n<h3> <strong>\u00d6rnek 3: Kusur say\u0131s\u0131<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Bir montaj hatt\u0131ndaki t\u00fcm par\u00e7alar\u0131n %5&#8217;inin kusurlu oldu\u011funun bilindi\u011fini varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">0, 1, 2 widget&#8217;\u0131 vb. inceleme olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in a\u015fa\u011f\u0131daki form\u00fclleri kullanabiliriz. Bir denet\u00e7i hatal\u0131 bir widget ile kar\u015f\u0131la\u015fmadan \u00f6nce:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=0)<\/strong> = (1-.05) <sup>0<\/sup> (.05) = <strong>0.05<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=1)<\/strong> = (1-0,05) <sup>1<\/sup> (0,05) = <strong>0,0475<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=2)<\/strong> = (1-0,05) <sup>2<\/sup> (0,05) = <strong>0,04512<\/strong><\/span><\/p>\n<h3> <strong>\u00d6rnek 4: \u0130flas say\u0131s\u0131<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Belirli bir bankay\u0131 ziyaret eden ki\u015filerin %4&#8217;\u00fcn\u00fcn bunu iflas ba\u015fvurusunda bulunmak i\u00e7in yapt\u0131\u011f\u0131n\u0131 bildi\u011fimizi varsayal\u0131m. Bir bankac\u0131n\u0131n, iflas etti\u011fini a\u00e7\u0131klayan biriyle tan\u0131\u015fmadan \u00f6nce 10&#8217;dan az ki\u015fiyle tan\u0131\u015fma olas\u0131l\u0131\u011f\u0131n\u0131 bilmek istedi\u011fini varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130flas eden biriyle kar\u015f\u0131la\u015fmadan \u00f6nce 10&#8217;dan az ki\u015fiyle tan\u0131\u015fma olas\u0131l\u0131\u011f\u0131n\u0131n <strong>0,33517<\/strong> oldu\u011funu bulmak i\u00e7in p = 0,04 ve x = 10 olan<a href=\"https:\/\/statorials.org\/tr\/geometrik-dagilim-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">geometrik da\u011f\u0131l\u0131m hesaplay\u0131c\u0131s\u0131n\u0131<\/a> kullanabiliriz.<\/span><\/p>\n<h3> <strong>\u00d6rnek 5: A\u011f kesintilerinin say\u0131s\u0131<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Belirli bir \u015firketin belirli bir haftada a\u011f kesintisi ya\u015fama olas\u0131l\u0131\u011f\u0131n\u0131n %10 oldu\u011funu bildi\u011fimizi varsayal\u0131m. \u015eirketin CEO&#8217;sunun, \u015firketin a\u011f kesintisi ya\u015famadan 5 hafta veya daha uzun s\u00fcre dayanabilme olas\u0131l\u0131\u011f\u0131n\u0131 bilmek istedi\u011fini varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130\u015fin ba\u015far\u0131s\u0131zl\u0131kla sonu\u00e7lanmadan 5 hafta veya daha uzun s\u00fcre dayanma olas\u0131l\u0131\u011f\u0131n\u0131n <strong>0,59049<\/strong> oldu\u011funu bulmak i\u00e7in p = 0,10 ve x = 5 olan<a href=\"https:\/\/statorials.org\/tr\/geometrik-dagilim-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">geometrik da\u011f\u0131l\u0131m hesaplay\u0131c\u0131s\u0131n\u0131<\/a> kullanabiliriz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/tr\/normal-dagilim-ornegi\/\" target=\"_blank\" rel=\"noopener\">Normal da\u011f\u0131l\u0131m\u0131n 6 somut \u00f6rne\u011fi<\/a><br \/><a href=\"https:\/\/statorials.org\/tr\/binom-dagilimi-gercek-ornekleri\/\" target=\"_blank\" rel=\"noopener\">Binom da\u011f\u0131l\u0131m\u0131n\u0131n 5 somut \u00f6rne\u011fi<\/a><br \/><a href=\"https:\/\/statorials.org\/tr\/balik-dagitimi-gercek-ornekleri\/\" target=\"_blank\" rel=\"noopener\">Poisson da\u011f\u0131l\u0131m\u0131n\u0131n 5 somut \u00f6rne\u011fi<\/a><br \/><a href=\"https:\/\/statorials.org\/tr\/duzgun-dagilim-gercek-ornekleri\/\" target=\"_blank\" rel=\"noopener\">D\u00fczg\u00fcn da\u011f\u0131l\u0131ma 5 somut \u00f6rnek<\/a><\/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 modellemek i\u00e7in kullan\u0131lan bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r. Bernoulli denemesi yaln\u0131zca iki olas\u0131 sonucu olan bir deneydir: \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;, [&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-1614","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 5 somut \u00f6rnek<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde istatistikte en s\u0131k kullan\u0131lan da\u011f\u0131l\u0131mlardan biri olan geometrik da\u011f\u0131l\u0131ma ili\u015fkin ger\u00e7ek d\u00fcnyadan birka\u00e7 \u00f6rnek sunulmaktad\u0131r.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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