{"id":43,"date":"2023-08-06T06:29:55","date_gmt":"2023-08-06T06:29:55","guid":{"rendered":"https:\/\/statorials.org\/tr\/ampirik-olasilik\/"},"modified":"2023-08-06T06:29:55","modified_gmt":"2023-08-06T06:29:55","slug":"ampirik-olasilik","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ampirik-olasilik\/","title":{"rendered":"Ampirik olas\u0131l\u0131k"},"content":{"rendered":"

Bu yaz\u0131da ampirik olas\u0131l\u0131\u011f\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 a\u00e7\u0131kl\u0131yoruz. Ampirik olas\u0131l\u0131\u011f\u0131n ne oldu\u011funu, form\u00fcl\u00fcn\u00fcn ne oldu\u011funu, bir \u00f6rne\u011fini ve ampirik olas\u0131l\u0131k ile teorik olas\u0131l\u0131k aras\u0131ndaki farklar\u0131n neler oldu\u011funu ke\u015ffedeceksiniz. <\/p>\n

<\/span> Ampirik olas\u0131l\u0131k nedir?<\/span><\/h2>\n

Ampirik olas\u0131l\u0131k,<\/strong> bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 g\u00f6steren ampirik deneylere veya ger\u00e7eklere dayanan istatistiksel bir \u00f6l\u00e7\u00fcmd\u00fcr.<\/p>\n

Ba\u015fka bir deyi\u015fle ampirik olas\u0131l\u0131k, bir deneyin sonu\u00e7lar\u0131ndan hesaplan\u0131r ve bize bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 s\u00f6yler.<\/p>\n

Deney ne kadar \u00e7ok tekrarlan\u0131rsa elde edilen ampirik olas\u0131l\u0131k o kadar kesin olacakt\u0131r. Bu nedenle bu t\u00fcr olas\u0131l\u0131klar genellikle binlerce tekrar\u0131 sim\u00fcle eden ve \u00e7ok k\u0131sa s\u00fcrede analiz edebilen bilgisayar programlar\u0131 kullan\u0131larak belirlenir.<\/p>\n

Ampirik olas\u0131l\u0131k, 0 ile 1 aras\u0131nda bir say\u0131d\u0131r. Bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131 ne kadar y\u00fcksekse, ampirik olas\u0131l\u0131k da o kadar y\u00fcksektir ve bunun tersine, bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131 ne kadar d\u00fc\u015f\u00fckse, ampirik olas\u0131l\u0131k da o kadar d\u00fc\u015f\u00fckt\u00fcr. <\/p>\n

<\/span> Ampirik olas\u0131l\u0131k form\u00fcl\u00fc<\/span><\/h2>\n

Ampirik olas\u0131l\u0131k form\u00fcl\u00fc,<\/strong> bir deney s\u0131ras\u0131nda bir olay\u0131n meydana gelme say\u0131s\u0131n\u0131n deneyin ger\u00e7ekle\u015ftirilme toplam say\u0131s\u0131na b\u00f6l\u00fcnmesiyle elde edilir.<\/p>\n<\/p>\n

\"P=\\cfrac{\\text{veces<\/p>\n<\/p>\n

\u00d6rne\u011fin, bir a\u011faca on farkl\u0131 kez bakarsak ve a\u011fa\u00e7ta yedi kez bir ku\u015f g\u00f6r\u00fcrsek, a\u011faca bakarken bir ku\u015f g\u00f6rmenin ampirik olas\u0131l\u0131\u011f\u0131 \u015f\u00f6yle olacakt\u0131r: <\/p>\n<\/p>\n

\"P=\\cfrac{7}{10}=0,7\"<\/p>\n<\/p>\n

<\/span> Ampirik Olas\u0131l\u0131k \u00d6rne\u011fi<\/span><\/h2>\n

Ampirik olas\u0131l\u0131\u011f\u0131n tan\u0131m\u0131n\u0131 g\u00f6z \u00f6n\u00fcnde bulundurarak, bu t\u00fcr olas\u0131l\u0131klarla ilgili ad\u0131m ad\u0131m bir al\u0131\u015ft\u0131rma \u00e7\u00f6zece\u011fiz. Bu \u015fekilde ampirik olas\u0131l\u0131\u011f\u0131n nas\u0131l hesapland\u0131\u011f\u0131n\u0131 g\u00f6rebilirsiniz.<\/p>\n

    \n
  • Bir zar\u0131n at\u0131lmas\u0131yla ilgili rastgele deneyini olu\u015fturan temel olaylar\u0131n ampirik olas\u0131l\u0131\u011f\u0131n\u0131 hesaplar.<\/li>\n<\/ul>\n

    \u00d6ncelikle elde edilen deneysel sonu\u00e7lar\u0131 teorik sonu\u00e7larla kar\u015f\u0131la\u015ft\u0131rman\u0131n teorik olas\u0131l\u0131\u011f\u0131n\u0131 hesaplayaca\u011f\u0131z. 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=\\cfrac{1}{6}=0,167\"<\/p>\n<\/p>\n

    Bu al\u0131\u015ft\u0131rmay\u0131 \u00e7\u00f6zmek i\u00e7in, bir zar\u0131n birka\u00e7 kez at\u0131lmas\u0131n\u0131 sim\u00fcle etmemiz ve sonu\u00e7lar\u0131 bir olas\u0131l\u0131k tablosuna kaydetmemiz gerekir. Bunun i\u00e7in \u00f6rne\u011fin Excel program\u0131n\u0131 kullanabiliriz.<\/p>\n

    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 bir zar\u0131n ilk 10 rastgele at\u0131\u015f\u0131n\u0131n sim\u00fclasyonundan elde edilen sonu\u00e7lar a\u015fa\u011f\u0131daki gibidir: <\/p>\n

    \n
    \"ampirik<\/figure>\n<\/div>\n

    G\u00f6rd\u00fc\u011f\u00fcn\u00fcz gibi sadece on at\u0131\u015f sim\u00fcle edilerek elde edilen ampirik olas\u0131l\u0131klar teorik olas\u0131l\u0131klara (0,167) yak\u0131n de\u011fildir.<\/p>\n

    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

    \n
    \"ampirik<\/figure>\n<\/div>\n

    Art\u0131k zardaki her say\u0131 i\u00e7in hesaplanan ampirik olas\u0131l\u0131k teorik olas\u0131l\u0131\u011fa daha \u00e7ok benzer, ancak yine de \u00e7ok farkl\u0131 de\u011ferler elde ediyoruz.<\/p>\n

    Son olarak ayn\u0131 i\u015flemi yap\u0131yoruz ancak 1000 ba\u015flatmay\u0131 sim\u00fcle ediyoruz: <\/p>\n

    \n
    \"ampirik<\/figure>\n<\/div>\n

    Son beklenmedik durum tablosunda da g\u00f6rebilece\u011fimiz gibi art\u0131k ampirik olas\u0131l\u0131klar\u0131n de\u011ferleri teorik olas\u0131l\u0131klara \u00e7ok yak\u0131n.<\/p>\n

    \u00d6zetle, yap\u0131lan deneylerin say\u0131s\u0131 ne kadar artarsa, bir olay\u0131n ampirik olas\u0131l\u0131\u011f\u0131n\u0131n de\u011feri o olay\u0131n teorik ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131na o kadar yak\u0131n olacakt\u0131r<\/strong> . Bu kural, ne kadar \u00e7ok veri varsa deneysel de\u011ferlerin teorik de\u011ferlere o kadar yak\u0131n olaca\u011f\u0131n\u0131 ifade eden b\u00fcy\u00fck say\u0131lar kanunu<\/strong> olarak tan\u0131mlan\u0131r.<\/p>\n

    Ayr\u0131ca \u00fc\u00e7 frekans tablosunu kar\u015f\u0131la\u015ft\u0131rd\u0131\u011f\u0131m\u0131zda ampirik olas\u0131l\u0131\u011f\u0131n kesin olmad\u0131\u011f\u0131n\u0131 ancak yap\u0131lan deney say\u0131s\u0131na ba\u011fl\u0131 olarak de\u011fi\u015fti\u011fini g\u00f6r\u00fcyoruz. Bu, elde edilen de\u011ferleri nas\u0131l yorumlayaca\u011f\u0131n\u0131z\u0131 bilmeniz gerekti\u011fi anlam\u0131na gelir. <\/p>\n

    <\/span> Ampirik olas\u0131l\u0131k ve teorik olas\u0131l\u0131k<\/span><\/h2>\n

    Son olarak ampirik olas\u0131l\u0131k ve teorik olas\u0131l\u0131k kavramlar\u0131n\u0131 analiz edece\u011fiz \u00e7\u00fcnk\u00fc bunlar iki t\u00fcr olas\u0131l\u0131k olmas\u0131na ra\u011fmen tamamen farkl\u0131 anlamlara sahiptirler.<\/p>\n

    Ampirik olas\u0131l\u0131k ile teorik olas\u0131l\u0131k (veya klasik olas\u0131l\u0131k) aras\u0131ndaki fark<\/strong> , ampirik olas\u0131l\u0131\u011f\u0131n ger\u00e7ek deneyimlerden toplanan verilerden hesaplanmas\u0131, teorik olas\u0131l\u0131\u011f\u0131n ise herhangi bir deney yap\u0131lmadan ideal ko\u015fullar dikkate al\u0131narak hesaplanmas\u0131d\u0131r.<\/p>\n

    Yani ampirik olas\u0131l\u0131\u011f\u0131 bulmak i\u00e7in bir deneyin sim\u00fcle edilmesi ve hesaplaman\u0131n elde edilen sonu\u00e7lara g\u00f6re yap\u0131lmas\u0131 gerekir. Ancak teorik olas\u0131l\u0131\u011f\u0131 bilmek i\u00e7in hi\u00e7bir deney yap\u0131lmamal\u0131, bunun yerine teorik bir hesaplama yap\u0131lmal\u0131d\u0131r.<\/p>\n

    Ek olarak \u00f6nyarg\u0131 d\u00fczeyi<\/strong> ampirik olas\u0131l\u0131k ile teorik olas\u0131l\u0131k aras\u0131ndaki fark olarak tan\u0131mlan\u0131r. \u00d6nyarg\u0131 pozitif ya da negatif olabilir, ancak s\u0131f\u0131r olmas\u0131 \u00e7ok zordur \u00e7\u00fcnk\u00fc bu, rastgele bir deneyin teorik olas\u0131l\u0131\u011fa ula\u015fmas\u0131 anlam\u0131na gelir ki bu da pek olas\u0131 de\u011fildir.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Bu yaz\u0131da ampirik olas\u0131l\u0131\u011f\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 a\u00e7\u0131kl\u0131yoruz. Ampirik olas\u0131l\u0131\u011f\u0131n ne oldu\u011funu, form\u00fcl\u00fcn\u00fcn ne oldu\u011funu, bir \u00f6rne\u011fini ve ampirik olas\u0131l\u0131k ile teorik olas\u0131l\u0131k aras\u0131ndaki farklar\u0131n neler oldu\u011funu ke\u015ffedeceksiniz. Ampirik olas\u0131l\u0131k nedir? Ampirik olas\u0131l\u0131k, bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 g\u00f6steren ampirik deneylere veya ger\u00e7eklere dayanan istatistiksel bir \u00f6l\u00e7\u00fcmd\u00fcr. Ba\u015fka bir deyi\u015fle ampirik olas\u0131l\u0131k, bir deneyin sonu\u00e7lar\u0131ndan hesaplan\u0131r […]<\/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-43","post","type-post","status-publish","format-standard","hentry","category-olasilik"],"yoast_head":"\n\u25b7 Ampirik olas\u0131l\u0131k: tan\u0131m, form\u00fcl, \u00f6rnekler,...<\/title>\n<meta name=\"description\" content=\"Ampirik olas\u0131l\u0131k nedir ve nas\u0131l hesaplan\u0131r (form\u00fcl). Ampirik olas\u0131l\u0131k \u00f6rnekleriyle. 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Daha fazlas\u0131n\u0131 bil","sameAs":["https:\/\/statorials.org\/tr"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/posts\/43","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/comments?post=43"}],"version-history":[{"count":0,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/posts\/43\/revisions"}],"wp:attachment":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/media?parent=43"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/categories?post=43"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/tags?post=43"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}