{"id":19,"date":"2023-08-06T19:22:59","date_gmt":"2023-08-06T19:22:59","guid":{"rendered":"https:\/\/statorials.org\/tr\/ayrik-ornekleme-alani\/"},"modified":"2023-08-06T19:22:59","modified_gmt":"2023-08-06T19:22:59","slug":"ayrik-ornekleme-alani","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ayrik-ornekleme-alani\/","title":{"rendered":"Ayr\u0131k \u00f6rnek uzay"},"content":{"rendered":"

Ayr\u0131k \u00f6rnek uzay\u0131n ne oldu\u011funu ve ayr\u0131k \u00f6rnek uzay t\u00fcrlerinin neler oldu\u011funu her birinin \u00f6rnekleriyle a\u00e7\u0131kl\u0131yoruz. <\/p>\n

<\/span> Ayr\u0131k \u00f6rnek uzay nedir?<\/span><\/h2>\n

Olas\u0131l\u0131k teorisinde ayr\u0131k bir \u00f6rnek uzay<\/strong> , sonu\u00e7lar\u0131n\u0131n say\u0131s\u0131 sonlu veya say\u0131labilir olan rastgele bir deneydeki olaylar k\u00fcmesidir.<\/p>\n

Dolay\u0131s\u0131yla iki t\u00fcr ayr\u0131k \u00f6rnek uzay vard\u0131r: sonlu ayr\u0131k \u00f6rnek uzay<\/strong> ve say\u0131labilir sonsuz ayr\u0131k \u00f6rnek uzay<\/strong> .<\/p>\n

A\u015fa\u011f\u0131da her bir \u00f6rnek uzay t\u00fcr\u00fcn\u00fcn tan\u0131m\u0131n\u0131 g\u00f6rece\u011fiz.<\/p>\n

Bu durumda, ayr\u0131k \u00f6rnek uzay, s\u00fcrekli \u00f6rnek uzaydan olas\u0131 temel olaylar\u0131n say\u0131s\u0131na g\u00f6re farkl\u0131l\u0131k g\u00f6sterir, \u00e7\u00fcnk\u00fc ayr\u0131k \u00f6rnek uzayda olaylar\u0131n say\u0131s\u0131 sonludur ve di\u011fer yandan s\u00fcrekli \u00f6rnek uzayda olaylar\u0131n say\u0131s\u0131 sonsuzdur. . .<\/p>\n

Ek olarak, ayr\u0131k \u00f6rnek uzaylar, t\u00fcm olas\u0131 olaylar\u0131n olas\u0131l\u0131klar\u0131n\u0131n toplam\u0131n\u0131n bire e\u015fit olmas\u0131 \u00f6zelli\u011fine sahiptir. <\/p>\n<\/p>\n

\"\\displaystyle<\/p>\n<\/p>\n

<\/span> Ayr\u0131k \u00f6rnek uzay t\u00fcrleri<\/span><\/h2>\n

\u0130ki farkl\u0131 t\u00fcrde ayr\u0131k \u00f6rnek uzay vard\u0131r: sonlu ayr\u0131k \u00f6rnek uzay ve sonsuz say\u0131labilir ayr\u0131k \u00f6rnek uzay. Daha sonra, her birinin ne oldu\u011funu ve her \u00f6rnek uzay t\u00fcr\u00fcn\u00fcn \u00f6rneklerini g\u00f6rece\u011fiz.<\/p>\n

<\/span> Gizli \u00f6rnek alan kaplamas\u0131<\/span><\/h3>\n

Olas\u0131 olaylar\u0131n say\u0131s\u0131 sonlu oldu\u011funda, yani olas\u0131 sonu\u00e7lar\u0131n say\u0131s\u0131 say\u0131sal olarak tan\u0131mland\u0131\u011f\u0131nda , \u00f6rnek uzay sonlu ayr\u0131kt\u0131r<\/strong> .<\/p>\n

\u00d6rne\u011fin, bir zar\u0131n at\u0131lmas\u0131 i\u00e7in \u00f6rnek uzay ayr\u0131k olarak sonludur \u00e7\u00fcnk\u00fc yaln\u0131zca alt\u0131 olay meydana gelebilir. Zar at\u0131lmadan \u00f6nce olas\u0131 olaylar\u0131n say\u0131s\u0131n\u0131 zaten bildi\u011fimiz i\u00e7in sonlu ayr\u0131k bir \u00f6rnek uzayla u\u011fra\u015f\u0131yoruz.<\/p>\n<\/p>\n

\"\\Omega=\\{1,2,3,4,5,6\\}\"<\/p>\n<\/p>\n

\u00dcstelik t\u00fcm olaylar\u0131n olas\u0131l\u0131\u011f\u0131 ayn\u0131ysa, bu e\u015fit olas\u0131l\u0131kl\u0131 ayr\u0131k bir \u00f6rnek uzayd\u0131r. \u00d6rne\u011fin, yaz\u0131 tura atma olas\u0131l\u0131\u011f\u0131n\u0131n %50 oldu\u011fu ve yaz\u0131 gelme olas\u0131l\u0131\u011f\u0131n\u0131n da ayn\u0131 oldu\u011fu bir yaz\u0131 tura atmak gibi. <\/p>\n

<\/span> Say\u0131labilir sonsuz ayr\u0131k \u00f6rnek uzay<\/span><\/h3>\n

Olas\u0131 sonu\u00e7lar\u0131n say\u0131s\u0131 say\u0131labilir \u015fekilde sonsuz<\/strong> oldu\u011funda, yani olas\u0131 sonu\u00e7lar\u0131n say\u0131s\u0131 say\u0131labilir ancak ger\u00e7ekle\u015ftirilecek toplam deney say\u0131s\u0131 ve dolay\u0131s\u0131yla olas\u0131 sonu\u00e7lar\u0131n toplam say\u0131s\u0131 bilinmedi\u011finde, \u00f6rnek uzay ayr\u0131k say\u0131labilir \u015fekilde sonsuzdur.<\/p>\n

\u00d6rne\u011fin, zarlar\u0131 \u00fcst y\u00fczleri alt\u0131 g\u00f6sterene kadar atma deneyi say\u0131labilir \u015fekilde sonsuz ayr\u0131k bir \u00f6rnek uzaya sahiptir, \u00e7\u00fcnk\u00fc olas\u0131 temel olaylar say\u0131labilir ama ayn\u0131 zamanda sonsuzdur (ka\u00e7 kez zar atmam\u0131z gerekti\u011fini bilmiyoruz) alt\u0131 almak i\u00e7in zar).<\/p>\n<\/p>\n

\"\\Omega=\\{1,2,3,...\\}\"<\/p><\/p>\n","protected":false},"excerpt":{"rendered":"

Ayr\u0131k \u00f6rnek uzay\u0131n ne oldu\u011funu ve ayr\u0131k \u00f6rnek uzay t\u00fcrlerinin neler oldu\u011funu her birinin \u00f6rnekleriyle a\u00e7\u0131kl\u0131yoruz. Ayr\u0131k \u00f6rnek uzay nedir? Olas\u0131l\u0131k teorisinde ayr\u0131k bir \u00f6rnek uzay , sonu\u00e7lar\u0131n\u0131n say\u0131s\u0131 sonlu veya say\u0131labilir olan rastgele bir deneydeki olaylar k\u00fcmesidir. Dolay\u0131s\u0131yla iki t\u00fcr ayr\u0131k \u00f6rnek uzay vard\u0131r: sonlu ayr\u0131k \u00f6rnek uzay ve say\u0131labilir sonsuz ayr\u0131k \u00f6rnek uzay […]<\/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-19","post","type-post","status-publish","format-standard","hentry","category-olasilik"],"yoast_head":"\n\u25b7 Ayr\u0131k \u00f6rnek uzay nedir? 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