{"id":3936,"date":"2023-07-14T16:01:08","date_gmt":"2023-07-14T16:01:08","guid":{"rendered":"https:\/\/statorials.org\/tr\/beklenen-deger-x3\/"},"modified":"2023-07-14T16:01:08","modified_gmt":"2023-07-14T16:01:08","slug":"beklenen-deger-x3","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/beklenen-deger-x3\/","title":{"rendered":"X^3&#39;\u00fcn beklenen de\u011feri nas\u0131l hesaplan\u0131r?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">X ile g\u00f6sterilen bir <a href=\"https:\/\/statorials.org\/tr\/rastgele-degiskenler\/\" target=\"_blank\" rel=\"noopener\">rastgele de\u011fi\u015fken<\/a> i\u00e7in, <sup>X3&#8217;\u00fcn<\/sup> beklenen de\u011ferini hesaplamak amac\u0131yla a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabilirsiniz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>E(X <sup>3<\/sup> ) = \u03a3x <sup>3<\/sup> * p(x)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03a3<\/strong> : \u201cToplam\u201d anlam\u0131na gelen bir sembol<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x<\/strong> : Rastgele de\u011fi\u015fkenin de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p(x)<\/strong> : Rasgele de\u011fi\u015fkenin verilen bir de\u011feri alma olas\u0131l\u0131\u011f\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekte bu form\u00fcl\u00fcn pratikte nas\u0131l kullan\u0131laca\u011f\u0131 g\u00f6sterilmektedir.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u00d6rnek: X <sup>3&#8217;\u00fcn<\/sup> beklenen de\u011ferinin hesaplanmas\u0131<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Bir rastgele de\u011fi\u015fkenin olas\u0131l\u0131\u011f\u0131n\u0131 tan\u0131mlayan a\u015fa\u011f\u0131daki olas\u0131l\u0131k da\u011f\u0131l\u0131m tablosuna sahip oldu\u011fumuzu varsayal\u0131m:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-31621 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/x2_1.jpg\" alt=\"\" width=\"266\" height=\"253\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">X <sup>3&#8217;\u00fcn<\/sup> beklenen de\u011ferini hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\">E(X <sup>3<\/sup> ) = \u03a3x <sup>3<\/sup> * p(x)<\/span><\/p>\n<p> <span style=\"color: #000000;\">E(X <sup>3<\/sup> ) = (0) <sup>3<\/sup> *.06 + (1) <sup>3<\/sup> *.15 + (2) <sup>3<\/sup> *.17 + (3) <sup>3<\/sup> *.24 + (4) <sup>3<\/sup> *.23 + (5) <sup>3<\/sup> *.09 + (6) <sup>3<\/sup> *.06<\/span><\/p>\n<p> <span style=\"color: #000000;\">E( <sup>X3<\/sup> ) = 0 + 0,15 + 0,1,36 + 6,48 + 14,72 + 11,25 + 12,96<\/span><\/p>\n<p> <span style=\"color: #000000;\">E( <sup>X3<\/sup> ) = 45,596<\/span><\/p>\n<p> <span style=\"color: #000000;\">X <sup>3&#8217;\u00fcn<\/sup> beklenen de\u011feri <strong>45.596&#8217;d\u0131r<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu rastgele de\u011fi\u015fkenin <strong>ayr\u0131 bir rastgele de\u011fi\u015fken<\/strong> oldu\u011funu, yani yaln\u0131zca s\u0131n\u0131rl\u0131 say\u0131da de\u011fer alabilece\u011fini unutmay\u0131n.<\/span><\/p>\n<p> <span style=\"color: #000000;\">E\u011fer X <strong>s\u00fcrekli bir rastgele de\u011fi\u015fkense<\/strong> , <sup>X3&#8217;\u00fcn<\/sup> beklenen de\u011ferini hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanmal\u0131y\u0131z:<\/span><\/p>\n<p> <strong><span style=\"color: #000000;\">E(X <sup>3<\/sup> ) = \u222b x <sup>3<\/sup> f(x)dx<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u222b: \u201cEntegrasyon\u201d anlam\u0131na gelen sembol<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>f(x)<\/strong> : <a href=\"https:\/\/statorials.org\/tr\/cdf-vs-pdf\/\" target=\"_blank\" rel=\"noopener\">PDF<\/a> rastgele de\u011fi\u015fken i\u00e7in devam ediyor<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Beklenen <sup>de\u011fer<\/sup> hesaplan\u0131rken<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimlerde istatistikteki di\u011fer genel g\u00f6revlerin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r:<\/span><\/p>\n<p><a href=\"https:\/\/statorials.org\/tr\/olasilik-dagiliminin-ortalamasi\/\" target=\"_blank\" rel=\"noopener\">Olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131 nas\u0131l bulunur?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/olasilik-dagiliminin-standart-sapmasi\/\" target=\"_blank\" rel=\"noopener\">Olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n standart sapmas\u0131 nas\u0131l bulunur?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/olasilik-dagiliminin-varyansi\/\" target=\"_blank\" rel=\"noopener\">Bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n varyans\u0131 nas\u0131l bulunur?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>X ile g\u00f6sterilen bir rastgele de\u011fi\u015fken i\u00e7in, X3&#8217;\u00fcn beklenen de\u011ferini hesaplamak amac\u0131yla a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabilirsiniz: E(X 3 ) = \u03a3x 3 * p(x) Alt\u0131n: \u03a3 : \u201cToplam\u201d anlam\u0131na gelen bir sembol x : Rastgele de\u011fi\u015fkenin de\u011feri p(x) : Rasgele de\u011fi\u015fkenin verilen bir de\u011feri alma olas\u0131l\u0131\u011f\u0131 A\u015fa\u011f\u0131daki \u00f6rnekte bu form\u00fcl\u00fcn pratikte nas\u0131l kullan\u0131laca\u011f\u0131 g\u00f6sterilmektedir. \u00d6rnek: X [&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-3936","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>X^3&#039;\u00fcn beklenen de\u011feri nas\u0131l hesaplan\u0131r - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde X^3&#039;\u00fcn beklenen de\u011ferinin nas\u0131l hesaplanaca\u011f\u0131 bir \u00f6rnekle a\u00e7\u0131klanmaktad\u0131r.\" \/>\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\/beklenen-deger-x3\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta 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