{"id":36,"date":"2023-08-06T10:13:35","date_gmt":"2023-08-06T10:13:35","guid":{"rendered":"https:\/\/statorials.org\/tr\/frekans-frekansi-olasiligi-1\/"},"modified":"2023-08-06T10:13:35","modified_gmt":"2023-08-06T10:13:35","slug":"frekans-frekansi-olasiligi-1","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/frekans-frekansi-olasiligi-1\/","title":{"rendered":"Frekans olas\u0131l\u0131\u011f\u0131 (veya frekans\u00e7\u0131)"},"content":{"rendered":"<p>Bu makalede bunun ne oldu\u011funu ve frekans olas\u0131l\u0131\u011f\u0131n\u0131n (veya frekans olas\u0131l\u0131\u011f\u0131n\u0131n) nas\u0131l hesaplanaca\u011f\u0131n\u0131 a\u00e7\u0131kl\u0131yoruz. Frekans olas\u0131l\u0131\u011f\u0131na ili\u015fkin bir \u00f6rnek bulacaks\u0131n\u0131z ve ayr\u0131ca frekans olas\u0131l\u0131\u011f\u0131 ile teorik olas\u0131l\u0131k aras\u0131ndaki fark\u0131n ne oldu\u011funu g\u00f6rebileceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-probabilidad-frecuencial\"><\/span> Frekans olas\u0131l\u0131\u011f\u0131 nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Frekans olas\u0131l\u0131\u011f\u0131<\/strong> olarak da adland\u0131r\u0131lan frekans <strong>olas\u0131l\u0131\u011f\u0131<\/strong> , rastgele bir deneydeki temel bir olay\u0131n uzun vadede beklenen ba\u011f\u0131l frekans\u0131d\u0131r.<\/p>\n<p> Bir olay\u0131n s\u0131kl\u0131k olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in deneyin \u00e7ok say\u0131da yap\u0131lmas\u0131 ve elde edilen olumlu durumlar\u0131n say\u0131s\u0131n\u0131n ger\u00e7ekle\u015ftirilen toplam tekrar say\u0131s\u0131na b\u00f6l\u00fcnmesi gerekir.<\/p>\n<p> Deney ne kadar \u00e7ok tekrarlan\u0131rsa elde edilen frekans olas\u0131l\u0131\u011f\u0131 o kadar kesin olacakt\u0131r. Dolay\u0131s\u0131yla bu t\u00fcr olas\u0131l\u0131klar genellikle binlerce tekrar\u0131 sim\u00fcle eden ve bunlar\u0131 \u00e7ok k\u0131sa s\u00fcrede analiz edebilen bilgisayar programlar\u0131 kullan\u0131larak hesaplan\u0131r.<\/p>\n<p> Matematiksel olarak, frekans olas\u0131l\u0131k form\u00fcl\u00fc, <em>N&#8217;nin<\/em> sonsuzdaki limitinin <em>s&#8217;ye<\/em> b\u00f6l\u00fcm\u00fcd\u00fcr; burada <em>N<\/em> <em>,<\/em> toplam deney say\u0131s\u0131 ve <em>s,<\/em> elde edilen olumlu durumlar\u0131n say\u0131s\u0131d\u0131r.<\/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-9ee8cdba2713256ce199da17fcb2235c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(s)=\\lim\\limits_{N\\to \\infty}\\cfrac{s}{N}\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"121\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> Form\u00fcl\u00fc anlamad\u0131ysan\u0131z endi\u015felenmeyin, \u00e7\u00fcnk\u00fc ayn\u0131 deneyi sonsuza kadar tekrarlamak m\u00fcmk\u00fcn de\u011fildir \u00e7\u00fcnk\u00fc onu asla bitiremeyiz. Bu, frekans olas\u0131l\u0131\u011f\u0131n\u0131n \u00e7ok say\u0131da tekrarla hesaplanmas\u0131 gerekti\u011fi anlam\u0131na gelir.<\/p>\n<p> G\u00f6rd\u00fc\u011f\u00fcn\u00fcz gibi frekans olas\u0131l\u0131\u011f\u0131, kavramsal olarak farkl\u0131 anlamlara gelse de ayn\u0131 ba\u011f\u0131l frekans form\u00fcl\u00fc kullan\u0131larak hesaplan\u0131yor. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-probabilidad-frecuencial\"><\/span> Frekans Olas\u0131l\u0131\u011f\u0131 \u00d6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Konsepti daha iyi anlamak i\u00e7in bir al\u0131\u015ft\u0131rmay\u0131 ad\u0131m ad\u0131m \u00e7\u00f6zerek frekans olas\u0131l\u0131\u011f\u0131n\u0131n nas\u0131l hesapland\u0131\u011f\u0131n\u0131 g\u00f6rece\u011fiz. Neyse frekans ihtimalinin anlam\u0131n\u0131 anlamak kolay olmad\u0131\u011f\u0131ndan sorular\u0131n\u0131z varsa a\u015fa\u011f\u0131ya yorum olarak b\u0131rakabilirsiniz.<\/p>\n<ul>\n<li> Zar\u0131n at\u0131lmas\u0131ndaki rastgele deneyimi olu\u015fturan temel olaylar\u0131n s\u0131kl\u0131k olas\u0131l\u0131\u011f\u0131n\u0131 hesaplay\u0131n.<\/li>\n<\/ul>\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> Dolay\u0131s\u0131yla, bu al\u0131\u015ft\u0131rmay\u0131 \u00e7\u00f6zmek i\u00e7in f\u0131rlatmay\u0131 birka\u00e7 kez sim\u00fcle etmemiz ve sonu\u00e7lar\u0131 bir frekans tablosuna kaydetmemiz gerekiyor. \u00d6rne\u011fin Excel yaz\u0131l\u0131m\u0131n\u0131 kullanabilirsiniz.<\/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=\"frekans olas\u0131l\u0131\u011f\u0131 \u00f6rne\u011fi\" 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=\"s\u0131k olas\u0131l\u0131k \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=\"frekans olas\u0131l\u0131k al\u0131\u015ft\u0131rmas\u0131 \u00e7\u00f6z\u00fcld\u00fc\" 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, <strong>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 yak\u0131n olacakt\u0131r<\/strong> . Bu kural, yineleme say\u0131s\u0131 ne kadar fazla olursa deneysel de\u011ferlerin teorik de\u011ferlere o kadar benzeyece\u011fini belirten <strong><a href=\"https:\/\/statorials.org\/tr\/buyuk-sayilar-kanunu\/\">b\u00fcy\u00fck say\u0131lar kanunu<\/a><\/strong> olarak tan\u0131mlan\u0131r.<\/p>\n<p> Ek olarak, \u00fc\u00e7 frekans tablosunu kar\u015f\u0131la\u015ft\u0131r\u0131rsan\u0131z, frekans olas\u0131l\u0131\u011f\u0131n\u0131n kesin olmad\u0131\u011f\u0131n\u0131, yineleme say\u0131s\u0131na ba\u011fl\u0131 olarak de\u011fi\u015fti\u011fini g\u00f6rebilirsiniz. Bu nedenle elde edilen de\u011ferleri nas\u0131l yorumlayaca\u011f\u0131n\u0131z\u0131 bilmelisiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"probabilidad-frecuencial-y-probabilidad-teorica\"><\/span> Frekans olas\u0131l\u0131\u011f\u0131 ve teorik olas\u0131l\u0131k<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Frekans olas\u0131l\u0131\u011f\u0131 ile teorik olas\u0131l\u0131k (veya klasik olas\u0131l\u0131k) aras\u0131ndaki fark,<\/strong> frekans olas\u0131l\u0131\u011f\u0131n\u0131n deneysel sonu\u00e7lar kullan\u0131larak hesaplanmas\u0131 ve teorik olas\u0131l\u0131\u011f\u0131n ideal ko\u015fullardaki sonu\u00e7lar dikkate al\u0131narak hesaplanmas\u0131d\u0131r.<\/p>\n<p> Ba\u015fka bir deyi\u015fle frekans olas\u0131l\u0131\u011f\u0131n\u0131 bulmak i\u00e7in bir deneyin sim\u00fcle edilmesi ve elde edilen sonu\u00e7lardan hesaplama yap\u0131lmas\u0131 gerekir. Ancak teorik olas\u0131l\u0131\u011f\u0131 bilmek i\u00e7in deney yap\u0131lmamal\u0131, teorik bir hesaplama yap\u0131lmal\u0131d\u0131r.<\/p>\n<p> Frekans olas\u0131l\u0131k form\u00fcl\u00fc, bir deneyde elde edilen olumlu durumlar\u0131n say\u0131s\u0131n\u0131n toplam deneme say\u0131s\u0131na b\u00f6l\u00fcnmesiyle elde edilir.<\/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-d10bd148b769bd5e3c509ce78aaddb7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" P_f=\\cfrac{\\text{n\\'umero de casos favorables en el experimento}}{\\text{n\\'umero total de intentos}}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"400\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> Buna kar\u015f\u0131l\u0131k, teorik olas\u0131l\u0131k form\u00fcl\u00fc, olumlu olaylar\u0131n say\u0131s\u0131n\u0131n olas\u0131 temel olaylar\u0131n toplam say\u0131s\u0131na b\u00f6l\u00fcnmesiyle elde edilir.<\/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-c18f28689a1a137a6c9c52ff5b64ddf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" P_t=\\cfrac{\\text{n\\'umero de eventos favorables}}{\\text{n\\'umero total de eventos elementales}}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"324\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> Frekans olas\u0131l\u0131\u011f\u0131 esas olarak her temel olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131n bilinmedi\u011fi deneylerde kullan\u0131l\u0131r. Daha sonra bir\u00e7ok yineleme sim\u00fcle edilir ve her bir olay\u0131n ne s\u0131kl\u0131kta ger\u00e7ekle\u015fece\u011fini tahmin etmek i\u00e7in s\u0131kl\u0131k olas\u0131l\u0131klar\u0131 kullan\u0131l\u0131r.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede bunun ne oldu\u011funu ve frekans olas\u0131l\u0131\u011f\u0131n\u0131n (veya frekans olas\u0131l\u0131\u011f\u0131n\u0131n) nas\u0131l hesaplanaca\u011f\u0131n\u0131 a\u00e7\u0131kl\u0131yoruz. Frekans olas\u0131l\u0131\u011f\u0131na ili\u015fkin bir \u00f6rnek bulacaks\u0131n\u0131z ve ayr\u0131ca frekans olas\u0131l\u0131\u011f\u0131 ile teorik olas\u0131l\u0131k aras\u0131ndaki fark\u0131n ne oldu\u011funu g\u00f6rebileceksiniz. Frekans olas\u0131l\u0131\u011f\u0131 nedir? Frekans olas\u0131l\u0131\u011f\u0131 olarak da adland\u0131r\u0131lan frekans olas\u0131l\u0131\u011f\u0131 , rastgele bir deneydeki temel bir olay\u0131n uzun vadede beklenen ba\u011f\u0131l frekans\u0131d\u0131r. Bir [&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-36","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>\u25b7 Frekans olas\u0131l\u0131\u011f\u0131 (veya frekans\u00e7\u0131)<\/title>\n<meta name=\"description\" content=\"Frekans olas\u0131l\u0131\u011f\u0131n\u0131n (veya frekans olas\u0131l\u0131\u011f\u0131n\u0131n) ne oldu\u011funu ve nas\u0131l hesapland\u0131\u011f\u0131n\u0131 a\u00e7\u0131kl\u0131yoruz. 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