{"id":692,"date":"2023-07-29T02:06:34","date_gmt":"2023-07-29T02:06:34","guid":{"rendered":"https:\/\/statorials.org\/tr\/rastgele-degiskenler\/"},"modified":"2023-07-29T02:06:34","modified_gmt":"2023-07-29T02:06:34","slug":"rastgele-degiskenler","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/rastgele-degiskenler\/","title":{"rendered":"Rastgele de\u011fi\u015fkenler nelerdir?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Genellikle X ile g\u00f6sterilen <strong>rastgele<\/strong> <strong>de\u011fi\u015fken<\/strong> , olas\u0131 de\u011ferleri rastgele bir s\u00fcrecin sonu\u00e7lar\u0131 olan bir de\u011fi\u015fkendir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130ki t\u00fcr rastgele de\u011fi\u015fken vard\u0131r: <strong>kesikli<\/strong> ve <strong>s\u00fcrekli<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ayr\u0131k rastgele de\u011fi\u015fkenler<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>Ayr\u0131k bir rastgele de\u011fi\u015fken,<\/strong> yaln\u0131zca 0, 1, 2, 3, 4, 5\u2026100, 1 milyon vb. gibi say\u0131labilir say\u0131da farkl\u0131 de\u011fer alabilen bir de\u011fi\u015fkendir. Ayr\u0131k rastgele de\u011fi\u015fkenlere baz\u0131 \u00f6rnekler:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Bir paran\u0131n 20 kez at\u0131lmas\u0131ndan sonra yaz\u0131 gelme say\u0131s\u0131.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Bir zar\u0131n 100 kez at\u0131ld\u0131ktan sonra <em>4<\/em> rakam\u0131na gelme say\u0131s\u0131.<\/span><\/li>\n<li> <span style=\"color: #000000;\">50 widget&#8217;l\u0131k bir kutudaki kusurlu widget&#8217;lar\u0131n say\u0131s\u0131.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Ayr\u0131k bir rastgele de\u011fi\u015fken i\u00e7in <strong>olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131,<\/strong> bize rastgele de\u011fi\u015fkenin belirli de\u011ferleri alma olas\u0131l\u0131\u011f\u0131n\u0131 s\u00f6yler.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin adil bir zar\u0131 bir kez att\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m. X&#8217;in zar\u0131n belirli bir say\u0131ya d\u00fc\u015fme olas\u0131l\u0131\u011f\u0131n\u0131 g\u00f6stermesine izin verirsek olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 \u015fu \u015fekilde yaz\u0131labilir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>P(X=1):<\/strong> 1\/6<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>P(X=2):<\/strong> 1\/6<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>P(X=3):<\/strong> 1\/6<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>P(X=4):<\/strong> 1\/6<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>P(X=5):<\/strong> 1\/6<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>P(X=6):<\/strong> 1\/6<\/span><\/li>\n<\/ul>\n<blockquote>\n<p> <span style=\"color: #000000;\"><strong>Not:<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n ge\u00e7erli olabilmesi i\u00e7in a\u015fa\u011f\u0131daki iki kriteri kar\u015f\u0131lamas\u0131 gerekir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.<\/strong> Her sonucun olas\u0131l\u0131\u011f\u0131 0 ile 1 aras\u0131nda olmal\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2.<\/strong> T\u00fcm olas\u0131l\u0131klar\u0131n toplam\u0131 1 olmal\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Kal\u0131p rulosunun olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n bu kriterlerin her ikisini de kar\u015f\u0131lad\u0131\u011f\u0131n\u0131 unutmay\u0131n:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.<\/strong> Her sonucun olas\u0131l\u0131\u011f\u0131 0 ile 1 aras\u0131ndad\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2.<\/strong> T\u00fcm olas\u0131l\u0131klar\u0131n toplam\u0131 1&#8217;e e\u015fittir.<\/span><\/p>\n<\/blockquote>\n<p> <span style=\"color: #000000;\">Olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6rselle\u015ftirmek i\u00e7in bir histogram kullanabiliriz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-6659 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/variable-aleatoire1-2.png\" alt=\"Ayr\u0131k bir rastgele de\u011fi\u015fken i\u00e7in PDF\" width=\"461\" height=\"397\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Ayr\u0131k bir rastgele de\u011fi\u015fken i\u00e7in <strong>k\u00fcm\u00fclatif olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131,<\/strong> bize de\u011fi\u015fkenin belirli bir de\u011fere <em>e\u015fit veya daha d\u00fc\u015f\u00fck<\/em> bir de\u011fer alma olas\u0131l\u0131\u011f\u0131n\u0131 s\u00f6yler.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, bir zar at\u0131\u015f\u0131n\u0131n k\u00fcm\u00fclatif olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 \u015f\u00f6yle g\u00f6r\u00fcnecektir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>P(X\u22641):<\/strong> 1\/6<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>P(X\u22642):<\/strong> 2\/6<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>P(X\u22643):<\/strong> 3\/6<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>P(X\u22644):<\/strong> 4\/6<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>P(X\u22645):<\/strong> 5\/6<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>P(X\u22646):<\/strong> 6\/6<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Zar\u0131n bir veya daha az say\u0131ya gelme \u015fans\u0131 1\/6&#8217;d\u0131r, \u00e7\u00fcnk\u00fc birden daha k\u00fc\u00e7\u00fck bir say\u0131ya d\u00fc\u015femez.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130ki veya daha az yere d\u00fc\u015fme olas\u0131l\u0131\u011f\u0131 P(X=1) + P(X=2) = 1\/6 + 1\/6 = 2\/6&#8217;d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Benzer \u015fekilde, \u00fc\u00e7 veya daha az yere d\u00fc\u015fme olas\u0131l\u0131\u011f\u0131 P(X=1) + P(X=2) + P(X=3) = 1\/6 + 1\/6 + 1\/6 = 3\/6 , Ve yak\u0131nda.<\/span><\/p>\n<p> <span style=\"color: #000000;\">K\u00fcm\u00fclatif olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6rselle\u015ftirmek i\u00e7in bir histogram da kullanabiliriz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-6657\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/variable-aleatoire2.png\" alt=\"Ayr\u0131k bir rastgele de\u011fi\u015fken i\u00e7in CDF\" width=\"459\" height=\"370\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>S\u00fcrekli rastgele de\u011fi\u015fkenler<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>S\u00fcrekli rastgele de\u011fi\u015fken,<\/strong> sonsuz say\u0131da olas\u0131 de\u011fer alabilen bir de\u011fi\u015fkendir. S\u00fcrekli rastgele de\u011fi\u015fkenlere baz\u0131 \u00f6rnekler:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Bir hayvan\u0131n a\u011f\u0131rl\u0131\u011f\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\">Bir ki\u015finin y\u00fcksekli\u011fi<\/span><\/li>\n<li> <span style=\"color: #000000;\">Maraton ko\u015fmak i\u00e7in gereken s\u00fcre<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, bir ki\u015finin boyu 60,2 in\u00e7, 65,2344 in\u00e7, 70,431222 in\u00e7 vb. olabilir. Boyut i\u00e7in sonsuz say\u0131da olas\u0131 de\u011fer vard\u0131r.<\/span><\/p>\n<blockquote>\n<p> <span style=\"color: #000000;\"><strong>Genel kural:<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Sonu\u00e7lar\u0131n say\u0131s\u0131n\u0131 <i>sayabiliyorsan\u0131z<\/i> , ayr\u0131 bir rastgele de\u011fi\u015fkenle \u00e7al\u0131\u015f\u0131yorsunuz demektir; \u00f6rne\u011fin, bir madalyonun ka\u00e7 kez tura geldi\u011fini saymak gibi.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak sonucu <i>\u00f6l\u00e7ebiliyorsan\u0131z<\/i> , s\u00fcrekli bir rastgele de\u011fi\u015fkenle \u00e7al\u0131\u015f\u0131yorsunuz demektir; \u00f6rne\u011fin boy, kilo, zaman vb. \u00f6l\u00e7\u00fcm\u00fc.<\/span><\/p>\n<\/blockquote>\n<p> <span style=\"color: #000000;\">S\u00fcrekli bir rastgele de\u011fi\u015fken i\u00e7in <strong>olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131,<\/strong> bize rastgele de\u011fi\u015fkenin belirli de\u011ferleri alma olas\u0131l\u0131\u011f\u0131n\u0131 anlat\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bununla birlikte, ayr\u0131k rastgele de\u011fi\u015fkenlere y\u00f6nelik olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131ndan farkl\u0131 olarak, s\u00fcrekli bir rastgele de\u011fi\u015fkene y\u00f6nelik olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131, yaln\u0131zca de\u011fi\u015fkenin bir de\u011fer <em>aral\u0131\u011f\u0131n\u0131<\/em> alma olas\u0131l\u0131\u011f\u0131n\u0131 bize bildirmek i\u00e7in kullan\u0131labilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, belirli bir restorandaki hamburgerin \u00e7eyrek pound (0,25 pound) a\u011f\u0131rl\u0131\u011f\u0131nda olma olas\u0131l\u0131\u011f\u0131n\u0131 bilmek istedi\u011fimizi varsayal\u0131m. <em>A\u011f\u0131rl\u0131k<\/em> s\u00fcrekli bir de\u011fi\u015fken oldu\u011fundan sonsuz say\u0131da de\u011fer alabilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, belirli bir hamburgerin a\u011f\u0131rl\u0131\u011f\u0131 asl\u0131nda 0,250001 pound, 0,24 pound veya 0,2488 pound olabilir. Belirli bir hamburgerin tam olarak 0,25 pound a\u011f\u0131rl\u0131\u011f\u0131nda olma olas\u0131l\u0131\u011f\u0131 asl\u0131nda s\u0131f\u0131rd\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Dolay\u0131s\u0131yla bir hamburgerin a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 0,25 lbs&#8217;den az, 0,25 lbs&#8217;den fazla veya belirli bir aral\u0131kta (\u00f6rne\u011fin 0,23 lbs ile 0,27 lbs aras\u0131nda) olma olas\u0131l\u0131\u011f\u0131n\u0131 bize bildirmek i\u00e7in olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131 kullanabiliriz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimler rastgele de\u011fi\u015fkenler hakk\u0131nda ek bilgi sa\u011flar:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/iid-rastgele-degiskenler\/\" target=\"_blank\" rel=\"noopener\">iid rastgele de\u011fi\u015fkenler nelerdir?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/rastgele-degiskenler-gercek-ornekler\/\" target=\"_blank\" rel=\"noopener\">Ger\u00e7ek hayatta rastgele de\u011fi\u015fkenlere 10 \u00f6rnek<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Genellikle X ile g\u00f6sterilen rastgele de\u011fi\u015fken , olas\u0131 de\u011ferleri rastgele bir s\u00fcrecin sonu\u00e7lar\u0131 olan bir de\u011fi\u015fkendir. \u0130ki t\u00fcr rastgele de\u011fi\u015fken vard\u0131r: kesikli ve s\u00fcrekli . Ayr\u0131k rastgele de\u011fi\u015fkenler Ayr\u0131k bir rastgele de\u011fi\u015fken, yaln\u0131zca 0, 1, 2, 3, 4, 5\u2026100, 1 milyon vb. gibi say\u0131labilir say\u0131da farkl\u0131 de\u011fer alabilen bir de\u011fi\u015fkendir. Ayr\u0131k rastgele de\u011fi\u015fkenlere baz\u0131 \u00f6rnekler: [&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-692","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Rastgele de\u011fi\u015fkenler nelerdir? - Statorials<\/title>\n<meta name=\"description\" content=\"Resmi bir tan\u0131m ve birka\u00e7 \u00f6rnek i\u00e7eren, rastgele de\u011fi\u015fkenlerin basit bir a\u00e7\u0131klamas\u0131.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/tr\/rastgele-degiskenler\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Rastgele de\u011fi\u015fkenler nelerdir? - Statorials\" \/>\n<meta property=\"og:description\" content=\"Resmi bir tan\u0131m ve birka\u00e7 \u00f6rnek i\u00e7eren, rastgele de\u011fi\u015fkenlerin basit bir a\u00e7\u0131klamas\u0131.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/rastgele-degiskenler\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-29T02:06:34+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/variable-aleatoire1-2.png\" \/>\n<meta name=\"author\" content=\"Dr.benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr.benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/rastgele-degiskenler\/\",\"url\":\"https:\/\/statorials.org\/tr\/rastgele-degiskenler\/\",\"name\":\"Rastgele de\u011fi\u015fkenler nelerdir? - Statorials\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-07-29T02:06:34+00:00\",\"dateModified\":\"2023-07-29T02:06:34+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Resmi bir tan\u0131m ve birka\u00e7 \u00f6rnek i\u00e7eren, rastgele de\u011fi\u015fkenlerin basit bir a\u00e7\u0131klamas\u0131.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/rastgele-degiskenler\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/rastgele-degiskenler\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/rastgele-degiskenler\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Rastgele de\u011fi\u015fkenler nelerdir?\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/tr\/#website\",\"url\":\"https:\/\/statorials.org\/tr\/\",\"name\":\"Statorials\",\"description\":\"\u0130statistik okuryazarl\u0131\u011f\u0131 rehberiniz!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/tr\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"tr\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\",\"name\":\"Dr.benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"tr\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr.benjamin anderson\"},\"description\":\"Merhaba, ben Benjamin, emekli bir istatistik profes\u00f6r\u00fc ve Statorials \u00f6\u011fretmenine d\u00f6n\u00fc\u015ft\u00fcm. \u0130statistik alan\u0131ndaki kapsaml\u0131 deneyimim ve uzmanl\u0131\u011f\u0131mla, \u00f6\u011frencilerimi Statorials arac\u0131l\u0131\u011f\u0131yla g\u00fc\u00e7lendirmek i\u00e7in bilgilerimi payla\u015fmaya can at\u0131yorum. 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