{"id":389,"date":"2023-08-01T07:32:30","date_gmt":"2023-08-01T07:32:30","guid":{"rendered":"https:\/\/statorials.org\/tr\/buyuk-sayilar-kanunu-2\/"},"modified":"2023-08-01T07:32:30","modified_gmt":"2023-08-01T07:32:30","slug":"buyuk-sayilar-kanunu-2","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/buyuk-sayilar-kanunu-2\/","title":{"rendered":"B\u00fcy\u00fck say\u0131lar kanunu"},"content":{"rendered":"<p>Bu yaz\u0131m\u0131zda b\u00fcy\u00fck say\u0131lar kanununun ne oldu\u011funu, olas\u0131l\u0131k ve istatistikte ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131n\u0131 a\u00e7\u0131kl\u0131yoruz. Ayr\u0131ca b\u00fcy\u00fck say\u0131lar yasas\u0131n\u0131n uygulanmas\u0131na ili\u015fkin bir \u00f6rnek ve ayr\u0131ca bu yasa ile merkezi limit teoremi aras\u0131ndaki ili\u015fkinin ne oldu\u011funu g\u00f6rebileceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-ley-de-los-grandes-numeros\"><\/span> B\u00fcy\u00fck say\u0131lar kanunu nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Olas\u0131l\u0131k teorisinde <strong>b\u00fcy\u00fck say\u0131lar kanunu<\/strong> , \u00e7ok say\u0131da i\u015flemin sonucunu a\u00e7\u0131klayan bir kurald\u0131r. Daha spesifik olarak b\u00fcy\u00fck say\u0131lar kanunu, \u00e7ok say\u0131da denemeden elde edilen sonu\u00e7lar\u0131n ortalamas\u0131n\u0131n beklenen de\u011fere yak\u0131n olaca\u011f\u0131n\u0131 s\u00f6ylemektedir.<\/p>\n<p> Ayr\u0131ca b\u00fcy\u00fck say\u0131lar kanununa g\u00f6re ne kadar \u00e7ok deney yaparsak sonu\u00e7lar beklenen de\u011fere o kadar yak\u0131n olacakt\u0131r.<\/p>\n<p> \u00d6rne\u011fin, bir paray\u0131 be\u015f kez atarsak yaln\u0131zca bir kez (%20) tura gelebilir. Ancak, e\u011fer para birka\u00e7 kez at\u0131l\u0131rsa (1000&#8217;den fazla at\u0131\u015f), beklenen de\u011fer bu oldu\u011fundan, sonu\u00e7lar\u0131n neredeyse yar\u0131s\u0131 (%50) tura olacakt\u0131r. Bu b\u00fcy\u00fck say\u0131lar kanununun bir \u00f6rne\u011fidir.<\/p>\n<p> B\u00fcy\u00fck say\u0131lar yasas\u0131n\u0131n k\u00f6keni 16. y\u00fczy\u0131lda Gerolamo Cardano&#8217;ya dayanmaktad\u0131r, ancak tarih boyunca pek \u00e7ok yazar bu istatistik yasas\u0131n\u0131n geli\u015ftirilmesine kat\u0131lm\u0131\u015ft\u0131r: Bernoulli, Poisson, Chebyshev, Markov, Borel, Cantelli, Kolmogorov ve Khinchin. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/matematiksel-beklenti-veya-beklenen-deger\/\">Beklenen de\u011fer nedir?<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-ley-de-los-grandes-numeros\"><\/span> B\u00fcy\u00fck say\u0131lar yasas\u0131 \u00f6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> B\u00fcy\u00fck say\u0131lar yasas\u0131n\u0131n tan\u0131m\u0131n\u0131 g\u00f6rd\u00fckten sonra anlam\u0131n\u0131 daha iyi anlamak i\u00e7in somut bir \u00f6rnek g\u00f6rece\u011fiz. Bu durumda zar\u0131 atarak elde edebilece\u011fimiz olas\u0131 sonu\u00e7lar\u0131n olas\u0131l\u0131klar\u0131n\u0131 analiz edece\u011fiz.<\/p>\n<p> Bir zar at\u0131ld\u0131\u011f\u0131nda alt\u0131 olas\u0131 sonu\u00e7 vard\u0131r (1, 2, 3, 4, 5 ve 6), dolay\u0131s\u0131yla her temel olay\u0131n teorik olas\u0131l\u0131\u011f\u0131 \u015f\u00f6yledir:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d8d6889656fa0d5faf24bf66b58d9e27_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P=\\cfrac{1}{6}=0,167\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"116\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Daha sonra f\u0131rlatmay\u0131 birka\u00e7 kez sim\u00fcle edece\u011fiz ve b\u00fcy\u00fck say\u0131lar kanununa uyulup uyulmad\u0131\u011f\u0131n\u0131 kontrol etmek i\u00e7in sonu\u00e7lar\u0131 bir <a href=\"https:\/\/statorials.org\/tr\/frekans-tablosu\/\">frekans tablosuna<\/a> kaydedece\u011fiz.<\/p>\n<p> Ger\u00e7ekle\u015ftirilen deney say\u0131s\u0131n\u0131n \u00f6nemini g\u00f6rebilmeniz i\u00e7in, \u00f6nce on, sonra y\u00fcz ve son olarak da bin f\u0131rlatmay\u0131 sim\u00fcle edece\u011fiz. B\u00f6ylece 10 rastgele zar atma sim\u00fclasyonundan elde edilen sonu\u00e7lar a\u015fa\u011f\u0131daki gibidir: <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/exemple-de-probabilite-de-frequence.png\" alt=\"\" class=\"wp-image-568\" width=\"502\" height=\"196\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> G\u00f6rd\u00fc\u011f\u00fcn\u00fcz gibi sadece on at\u0131\u015f sim\u00fcle edilerek elde edilen frekans olas\u0131l\u0131klar\u0131 teorik olas\u0131l\u0131klara benzememektedir.<\/p>\n<p> Ancak deney say\u0131s\u0131n\u0131 art\u0131rd\u0131k\u00e7a bu iki \u00f6l\u00e7\u00fcm daha da benzer hale geliyor, 100 f\u0131rlatma sim\u00fclasyonuna bak\u0131n: <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/exemple-de-probabilite-frequentiste.png\" alt=\"b\u00fcy\u00fck say\u0131lar kanunu \u00f6rne\u011fi\" class=\"wp-image-570\" width=\"502\" height=\"192\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Art\u0131k zardaki her say\u0131 i\u00e7in hesaplanan frekans olas\u0131l\u0131\u011f\u0131 teorik olas\u0131l\u0131\u011fa daha \u00e7ok benziyor ancak yine de \u00e7ok farkl\u0131 de\u011ferler elde ediyoruz.<\/p>\n<p> Son olarak ayn\u0131 i\u015flemi yap\u0131yoruz ancak 1000 ba\u015flatmay\u0131 sim\u00fcle ediyoruz: <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/exercice-probabilite-resolu-frequent.png\" alt=\"b\u00fcy\u00fck say\u0131lar kanununun kararl\u0131 bir \u015fekilde uygulanmas\u0131\" class=\"wp-image-572\" width=\"503\" height=\"191\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Son tabloda g\u00f6rd\u00fc\u011f\u00fcm\u00fcz gibi art\u0131k frekans olas\u0131l\u0131klar\u0131n\u0131n de\u011ferleri teorik olas\u0131l\u0131klara \u00e7ok yak\u0131n.<\/p>\n<p> \u00d6zetle, yap\u0131lan deney say\u0131s\u0131n\u0131 ne kadar art\u0131r\u0131rsak, bir olay\u0131n frekans olas\u0131l\u0131\u011f\u0131n\u0131n de\u011feri o olay\u0131n teorik ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131na o kadar yakla\u015f\u0131r. Bu nedenle <strong>b\u00fcy\u00fck say\u0131lar yasas\u0131na<\/strong> uyulur, \u00e7\u00fcnk\u00fc ne kadar \u00e7ok yineleme yaparsak deneysel de\u011ferler teorik de\u011ferlere o kadar benzer olur. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/frekans-frekansi-olasiligi-1\/\">Frekans olas\u0131l\u0131\u011f\u0131<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"limitacion-de-la-ley-de-los-grandes-numeros\"><\/span> B\u00fcy\u00fck say\u0131lar yasas\u0131n\u0131n s\u0131n\u0131rland\u0131r\u0131lmas\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> B\u00fcy\u00fck say\u0131lar kanunu \u00e7o\u011fu durumda ge\u00e7erlidir, ancak baz\u0131 olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131 bu istatistiksel teoremi kar\u015f\u0131lamamaktad\u0131r.<\/p>\n<p> \u00d6rne\u011fin Cauchy da\u011f\u0131l\u0131m\u0131 veya Pareto da\u011f\u0131l\u0131m\u0131 (\u03b1&lt;1) deneme say\u0131s\u0131 artt\u0131k\u00e7a birbirine yak\u0131nsamamaktad\u0131r. Bunun nedeni da\u011f\u0131l\u0131mlar\u0131n kuyruklar\u0131n\u0131n b\u00fcy\u00fck olmas\u0131d\u0131r, bu da onlar\u0131n beklenen de\u011ferlerinin olmad\u0131\u011f\u0131 anlam\u0131na gelir.<\/p>\n<p> \u00d6te yandan, baz\u0131 deneyler \u00f6zelliklerinden dolay\u0131 \u00f6nyarg\u0131l\u0131d\u0131r, dolay\u0131s\u0131yla ara\u015ft\u0131rmac\u0131 sonu\u00e7lar\u0131 (kas\u0131tl\u0131 olarak ya da de\u011fil) rasyonel, psikolojik, ekonomik vb. i\u00e7in de\u011fi\u015ftirme e\u011filimindedir. sebepler. Bu durumlarda b\u00fcy\u00fck say\u0131lar kanunu \u00f6nyarg\u0131n\u0131n \u00e7\u00f6z\u00fclmesine yard\u0131mc\u0131 olmaz, ancak deneme say\u0131s\u0131 ne kadar artarsa arts\u0131n \u00f6nyarg\u0131 devam edecektir. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/olasilik-dagilim-turleri\/\">Olas\u0131l\u0131k da\u011f\u0131l\u0131m t\u00fcrleri<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ley-de-los-grandes-numeros-y-teorema-central-del-limite\"><\/span> B\u00fcy\u00fck say\u0131lar kanunu ve merkezi limit teoremi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> B\u00fcy\u00fck say\u0131lar yasas\u0131 ve merkezi limit teoremi, olas\u0131l\u0131k ve istatisti\u011fin birbiriyle yak\u0131ndan ili\u015fkili iki temel kural\u0131d\u0131r. Yani bu b\u00f6l\u00fcmde ili\u015fkilerinin ne oldu\u011funu ve farklar\u0131n\u0131n ne oldu\u011funu g\u00f6rece\u011fiz.<\/p>\n<p> Merkezi limit teoremi olarak da adland\u0131r\u0131lan merkezi limit teoremi, pop\u00fclasyonun olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131ndan ba\u011f\u0131ms\u0131z olarak, numune boyutu artt\u0131k\u00e7a numune ortalamalar\u0131n\u0131n da\u011f\u0131l\u0131m\u0131n\u0131n normal bir da\u011f\u0131l\u0131ma yakla\u015ft\u0131\u011f\u0131n\u0131 s\u00f6yler.<\/p>\n<p> <strong>B\u00fcy\u00fck say\u0131lar kanunu ile merkezi limit teoremi aras\u0131ndaki fark,<\/strong> b\u00fcy\u00fck say\u0131lar kanununun \u00e7ok say\u0131da denemenin ortalamas\u0131n\u0131n beklenen de\u011fere yak\u0131n oldu\u011funu s\u00f6ylemesi, ancak merkezi limit teoreminin bir\u00e7ok denemenin ortalamas\u0131n\u0131n beklenen de\u011fere yak\u0131n oldu\u011funu s\u00f6ylemesidir. \u00f6rnekler normal da\u011f\u0131l\u0131ma yak\u0131nd\u0131r. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/merkezi-limit-teoremi\/\">Merkezi limit teoremi<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu yaz\u0131m\u0131zda b\u00fcy\u00fck say\u0131lar kanununun ne oldu\u011funu, olas\u0131l\u0131k ve istatistikte ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131n\u0131 a\u00e7\u0131kl\u0131yoruz. Ayr\u0131ca b\u00fcy\u00fck say\u0131lar yasas\u0131n\u0131n uygulanmas\u0131na ili\u015fkin bir \u00f6rnek ve ayr\u0131ca bu yasa ile merkezi limit teoremi aras\u0131ndaki ili\u015fkinin ne oldu\u011funu g\u00f6rebileceksiniz. B\u00fcy\u00fck say\u0131lar kanunu nedir? Olas\u0131l\u0131k teorisinde b\u00fcy\u00fck say\u0131lar kanunu , \u00e7ok say\u0131da i\u015flemin sonucunu a\u00e7\u0131klayan bir kurald\u0131r. Daha spesifik olarak [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-389","post","type-post","status-publish","format-standard","hentry","category-olasilik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7B\u00fcy\u00fck say\u0131lar kanunu<\/title>\n<meta name=\"description\" content=\"Burada b\u00fcy\u00fck say\u0131lar yasas\u0131n\u0131n ne oldu\u011funu, ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131n\u0131, \u00e7\u00f6z\u00fcml\u00fc \u00f6rnekleri ve bu yasa ile merkezi limit teoremi aras\u0131ndaki ili\u015fkiyi bulacaks\u0131n\u0131z.\" \/>\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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