{"id":2154,"date":"2023-07-23T11:32:41","date_gmt":"2023-07-23T11:32:41","guid":{"rendered":"https:\/\/statorials.org\/tr\/olasilik-dagiliminin-varyansi\/"},"modified":"2023-07-23T11:32:41","modified_gmt":"2023-07-23T11:32:41","slug":"olasilik-dagiliminin-varyansi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/olasilik-dagiliminin-varyansi\/","title":{"rendered":"Olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n varyans\u0131 nas\u0131l hesaplan\u0131r"},"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;\">Bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n <b>varyans\u0131n\u0131<\/b> bulmak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabiliriz:<\/span><\/p>\n<p> <strong><span style=\"color: #000000;\">\u03c3 <sup>2<\/sup> = \u03a3(x <sub>ben<\/sub> -\u03bc) <sup>2<\/sup> * P(x <sub>ben<\/sub> )<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>x <sub>i<\/sub> :<\/strong> <sup>i&#8217;inci<\/sup> de\u011fer<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u03bc:<\/strong> Da\u011f\u0131l\u0131m\u0131n ortalamas\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>P(x <sub>i<\/sub> ):<\/strong> <sup>i&#8217;inci<\/sup> de\u011ferin olas\u0131l\u0131\u011f\u0131<\/span><\/li>\n<\/ul>\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;\">Daha sonra varyans\u0131 \u015fu \u015fekilde hesaplayabiliriz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14122 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/sddist1.png\" alt=\"Olas\u0131l\u0131k Da\u011f\u0131l\u0131m\u0131nda Standart Sapma \u00d6rne\u011fi\" width=\"482\" height=\"195\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Varyans basit\u00e7e \u00fc\u00e7\u00fcnc\u00fc s\u00fctundaki de\u011ferlerin toplam\u0131d\u0131r. Yani bunu \u015fu \u015fekilde hesaplayaca\u011f\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><sup>\u03c32<\/sup> = 0,3785 + 0,0689 + 0,1059 + 0,2643 + 0,1301 = <strong>0,9475<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler, bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n varyans\u0131n\u0131n di\u011fer birka\u00e7 senaryoda nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6stermektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 1: Ara\u00e7 ar\u0131zalar\u0131ndaki de\u011fi\u015fim<\/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;\">Bu olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n varyans\u0131n\u0131 bulmak i\u00e7in \u00f6ncelikle beklenen hatalar\u0131n ortalama say\u0131s\u0131n\u0131 hesaplamam\u0131z gerekir:<\/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<p> <span style=\"color: #000000;\">Daha sonra varyans\u0131 \u015fu \u015fekilde hesaplayabiliriz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14123\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/sddist2.png\" alt=\"Bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n standart sapmas\u0131n\u0131 ve varyans\u0131n\u0131 hesaplama \u00f6rne\u011fi\" width=\"447\" height=\"152\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Varyans \u00fc\u00e7\u00fcnc\u00fc s\u00fctundaki de\u011ferlerin toplam\u0131d\u0131r. Yani bunu \u015fu \u015fekilde hesaplayaca\u011f\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><sup>\u03c32<\/sup> = 0,2305 + 0,0002 + 0,1665 + 0,1224 = <strong>0,5196<\/strong><\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 2: Sat\u0131\u015f varyasyonu<\/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;\">Bu olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n varyans\u0131n\u0131 bulmak i\u00e7in \u00f6ncelikle beklenen sat\u0131\u015flar\u0131n ortalama say\u0131s\u0131n\u0131 hesaplamam\u0131z gerekir:<\/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<p> <span style=\"color: #000000;\">Daha sonra varyans\u0131 \u015fu \u015fekilde hesaplayabiliriz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14124 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/sddist3.png\" alt=\"\" width=\"461\" height=\"154\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Varyans \u00fc\u00e7\u00fcnc\u00fc s\u00fctundaki de\u011ferlerin toplam\u0131d\u0131r. Yani bunu \u015fu \u015fekilde hesaplayaca\u011f\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><sup>\u03c32<\/sup> = 38,7096 + 2,2599 + 20,7831 + 17,9574 = <strong>79,71<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu da\u011f\u0131l\u0131m\u0131n varyans\u0131n\u0131 otomatik olarak hesaplamak i\u00e7in olas\u0131l\u0131k da\u011f\u0131l\u0131m hesaplay\u0131c\u0131s\u0131n\u0131 da kullanabilece\u011fimizi unutmay\u0131n:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-19947 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/stdprob1.png\" alt=\"\" width=\"305\" height=\"517\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-19948 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/stdprob2.png\" alt=\"\" width=\"309\" height=\"186\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Fark <strong>79,71<\/strong> . Bu bizim manuel olarak hesaplad\u0131\u011f\u0131m\u0131z de\u011fere kar\u015f\u0131l\u0131k geliyor.<\/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: Bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n varyans\u0131n\u0131 bulmak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabiliriz: \u03c3 2 = \u03a3(x ben -\u03bc) 2 * P(x ben ) Alt\u0131n: x i : i&#8217;inci de\u011fer [&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-2154","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - 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