{"id":1426,"date":"2023-07-26T10:48:30","date_gmt":"2023-07-26T10:48:30","guid":{"rendered":"https:\/\/statorials.org\/tr\/olasilik-dagiliminin-ortalamasi\/"},"modified":"2023-07-26T10:48:30","modified_gmt":"2023-07-26T10:48:30","slug":"olasilik-dagiliminin-ortalamasi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/olasilik-dagiliminin-ortalamasi\/","title":{"rendered":"Olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131 nas\u0131l bulunur: \u00f6rneklerle"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 bize bir <a href=\"https:\/\/statorials.org\/tr\/rastgele-degiskenler\/\" target=\"_blank\" rel=\"noopener\">rastgele de\u011fi\u015fkenin<\/a> belirli de\u011ferleri alma olas\u0131l\u0131\u011f\u0131n\u0131 anlat\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, a\u015fa\u011f\u0131daki olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 bize belirli bir futbol tak\u0131m\u0131n\u0131n belirli bir ma\u00e7ta belirli say\u0131da gol atma olas\u0131l\u0131\u011f\u0131n\u0131 s\u00f6yler:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14093 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/moyennedist1.png\" alt=\"\" width=\"261\" height=\"185\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><em><strong>Not:<\/strong> Ge\u00e7erli bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131ndaki olas\u0131l\u0131klar\u0131n toplam\u0131 her zaman 1 olacakt\u0131r. Bu olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n ge\u00e7erli oldu\u011funu do\u011frulayabiliriz: 0,18 + 0,34 + 0,35 + 0,11 + 0,02 = 1.<\/em><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n <strong>ortalamas\u0131n\u0131<\/strong> (bazen &#8220;beklenen de\u011fer&#8221; olarak da adland\u0131r\u0131l\u0131r) bulmak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabiliriz:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 17px;\"> <strong><span style=\"color: #000000;\">Mean (Or \"Expected Value\") of a Probability Distribution:<\/span>\n\n<span style=\"color: #3366ff;\">\u03bc = \u03a3x * P(x)\n<\/span>\nwhere:\n<span style=\"color: #000000;\">\u2022x: Data value\n    \u2022P(x): Probability of value<\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin futbol tak\u0131m\u0131 i\u00e7in olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131m\u0131z\u0131 d\u00fc\u015f\u00fcn\u00fcn:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14093 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/moyennedist1.png\" alt=\"\" width=\"261\" height=\"185\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Futbol tak\u0131m\u0131n\u0131n ortalama gol say\u0131s\u0131 \u015fu \u015fekilde hesaplanacakt\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03bc = 0*0,18 + 1*0,34 + 2*0,35 + 3*0,11 + 4*0,02 = <strong>1,45<\/strong> gol.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler, di\u011fer birka\u00e7 senaryoda olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6stermektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 1: Ortalama ara\u00e7 ar\u0131za say\u0131s\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 bize belirli bir arac\u0131n 10 y\u0131ll\u0131k bir s\u00fcre boyunca belirli say\u0131da ak\u00fc ar\u0131zas\u0131 ya\u015fama olas\u0131l\u0131\u011f\u0131n\u0131 g\u00f6sterir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14097 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/moyennedist2.png\" alt=\"Olas\u0131l\u0131k Da\u011f\u0131l\u0131m\u0131n\u0131n Ortalamas\u0131n\u0131 Bulma \u00d6rne\u011fi\" width=\"265\" height=\"160\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>Soru:<\/strong> Bu ara\u00e7ta beklenen ortalama ar\u0131za say\u0131s\u0131 nedir?<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00c7\u00f6z\u00fcm:<\/strong> Beklenen ar\u0131zalar\u0131n ortalama say\u0131s\u0131 \u015fu \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03bc = 0*0,24 + 1*0,57 + 2*0,16 + 3*0,03 = <b>0,98<\/b> ba\u015far\u0131s\u0131zl\u0131k.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 2: ortalama galibiyet say\u0131s\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 bize belirli bir basketbol tak\u0131m\u0131n\u0131n bir turnuvada belirli say\u0131da oyun kazanma olas\u0131l\u0131\u011f\u0131n\u0131 g\u00f6sterir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14098 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/moyennedist3.png\" alt=\"Olas\u0131l\u0131k da\u011f\u0131l\u0131m ara\u00e7lar\u0131\" width=\"259\" height=\"240\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>Soru:<\/strong> Bu tak\u0131m i\u00e7in beklenen ortalama galibiyet say\u0131s\u0131 nedir?<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00c7\u00f6z\u00fcm:<\/strong> Beklenen kazan\u00e7lar\u0131n ortalama say\u0131s\u0131 \u015fu \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03bc = 0*0,06 + 1*0,15 + 2*0,17 + 3*0,24 + 4*0,23 + 5*0,09 + 6*0,06 = <b>2,94<\/b> kazan\u00e7.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 3: ortalama sat\u0131\u015f say\u0131s\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 bize belirli bir sat\u0131c\u0131n\u0131n gelecek ay belirli say\u0131da sat\u0131\u015f yapma olas\u0131l\u0131\u011f\u0131n\u0131 g\u00f6sterir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14099 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/moyennedist4.png\" alt=\"\" width=\"257\" height=\"150\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>Soru:<\/strong> Bu sat\u0131c\u0131n\u0131n \u00f6n\u00fcm\u00fczdeki ay ortalama sat\u0131\u015f say\u0131s\u0131 ne kadard\u0131r?<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00c7\u00f6z\u00fcm:<\/strong> Ortalama beklenen sat\u0131\u015f say\u0131s\u0131 \u015fu \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03bc = 10*0,24 + 20*0,31 + 30*0,39 + 40*0,06 = <b>22,7<\/b> kirli.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Bonus: Olas\u0131l\u0131k Da\u011f\u0131l\u0131m\u0131 Hesaplay\u0131c\u0131s\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Herhangi bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131n\u0131 otomatik olarak hesaplamak i\u00e7in bu hesaplay\u0131c\u0131y\u0131 kullanabilirsiniz.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 bize bir rastgele de\u011fi\u015fkenin belirli de\u011ferleri alma olas\u0131l\u0131\u011f\u0131n\u0131 anlat\u0131r. \u00d6rne\u011fin, a\u015fa\u011f\u0131daki olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 bize belirli bir futbol tak\u0131m\u0131n\u0131n belirli bir ma\u00e7ta belirli say\u0131da gol atma olas\u0131l\u0131\u011f\u0131n\u0131 s\u00f6yler: Not: Ge\u00e7erli bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131ndaki olas\u0131l\u0131klar\u0131n toplam\u0131 her zaman 1 olacakt\u0131r. Bu olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n ge\u00e7erli oldu\u011funu do\u011frulayabiliriz: 0,18 + 0,34 + 0,35 + 0,11 + 0,02 [&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-1426","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>Olas\u0131l\u0131k Da\u011f\u0131l\u0131m\u0131n\u0131n Ortalamas\u0131 Nas\u0131l Bulunur (\u00d6rneklerle) - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, kullan\u0131lacak bir form\u00fcl ve \u00e7e\u015fitli \u00f6rnekler de dahil olmak \u00fczere herhangi bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131n\u0131n nas\u0131l bulunaca\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r.\" \/>\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\/olasilik-dagiliminin-ortalamasi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Olas\u0131l\u0131k Da\u011f\u0131l\u0131m\u0131n\u0131n Ortalamas\u0131 Nas\u0131l Bulunur (\u00d6rneklerle) - 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