{"id":2426,"date":"2023-07-22T08:11:42","date_gmt":"2023-07-22T08:11:42","guid":{"rendered":"https:\/\/statorials.org\/tr\/beklenen-deger-gercek-ornekler\/"},"modified":"2023-07-22T08:11:42","modified_gmt":"2023-07-22T08:11:42","slug":"beklenen-deger-gercek-ornekler","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/beklenen-deger-gercek-ornekler\/","title":{"rendered":"Ger\u00e7ek hayatta beklenen de\u011ferin hesaplanmas\u0131na i\u0307li\u015fkin 5 \u00f6rnek"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Beklenen de\u011fer,<\/strong> <a href=\"https:\/\/statorials.org\/tr\/rastgele-degiskenler\/\" target=\"_blank\" rel=\"noopener\">bir rastgele de\u011fi\u015fkenin<\/a> sonsuz say\u0131da denemede alaca\u011f\u0131 beklenen ortalamay\u0131 bize s\u00f6yleyen bir de\u011ferdir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir olay\u0131n beklenen de\u011ferini hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullan\u0131r\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Beklenen de\u011fer<\/strong> = \u03a3x * P(x)<\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>x<\/strong> : veri de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>P(x)<\/strong> : De\u011fer olas\u0131l\u0131\u011f\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu form\u00fcl biraz kafa kar\u0131\u015ft\u0131r\u0131c\u0131 g\u00f6r\u00fcnebilir ancak ger\u00e7ek d\u00fcnyadaki \u00f6rnekler ba\u011flam\u0131nda kullan\u0131ld\u0131\u011f\u0131n\u0131 g\u00f6rd\u00fc\u011f\u00fcn\u00fczde daha anlaml\u0131 olacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler, beklenen de\u011ferin be\u015f farkl\u0131 ger\u00e7ek d\u00fcnya durumunda nas\u0131l hesapland\u0131\u011f\u0131n\u0131 g\u00f6stermektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 1: Yat\u0131r\u0131mlar<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Beklenen de\u011fer genellikle ticaret \u015firketleri taraf\u0131ndan bir yat\u0131r\u0131m\u0131n beklenen k\u00e2r\u0131n\u0131 veya zarar\u0131n\u0131 belirlemek i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, belirli bir yat\u0131r\u0131m\u0131n 0,95 olas\u0131l\u0131kla y\u0131ll\u0131k %5 getiri sa\u011flayabildi\u011fini, ancak 0,05 olas\u0131l\u0131kla y\u0131ll\u0131k -%20 getiri de sa\u011flayabildi\u011fini varsayal\u0131m.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-21780 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/attendre11.png\" alt=\"\" width=\"219\" height=\"96\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bu yat\u0131r\u0131m\u0131n beklenen de\u011ferini \u015fu \u015fekilde hesaplayabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Beklenen de\u011fer = %5*,95 + (-%20)*,05 = <strong>%3,75<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu \u00f6zel yat\u0131r\u0131m\u0131n olumlu bir beklenen de\u011feri vard\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu, e\u011fer bu \u00f6zel yat\u0131r\u0131ma sonsuz say\u0131da yat\u0131r\u0131m yapsayd\u0131k, uzun vadeli ortalama y\u0131ll\u0131k %3,75 getiri bekleyece\u011fimiz anlam\u0131na gelir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 2: Hava Durumu<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Beklenen de\u011fer genellikle tar\u0131m \u015firketleri taraf\u0131ndan belirli bir mevsimde d\u00fc\u015fecek beklenen ya\u011fmur miktar\u0131n\u0131 belirlemek i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, 1 in\u00e7 ya\u011fmur ya\u011fma ihtimalinin %20 oldu\u011funu, 2 in\u00e7 ya\u011fmur ya\u011fma ihtimalinin %70 oldu\u011funu ve 3 in\u00e7 ya\u011fmur ya\u011fma ihtimalinin %10 oldu\u011funu varsayal\u0131m.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-21781 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/attendre12.png\" alt=\"\" width=\"236\" height=\"130\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Ya\u011fmur miktar\u0131n\u0131n beklenen de\u011ferini \u015fu \u015fekilde hesaplar\u0131z:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Beklenen de\u011fer = 0,2*1 + 0,7*2 + 0,1*3 = <strong>1,9 in\u00e7<\/strong><\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 3: \u015eans Oyunlar\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Beklenen de\u011fer genellikle oyuncular taraf\u0131ndan belirli bir oyunda potansiyel olarak ne kadar kazanabileceklerini belirlemek i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, belirli bir oyunda 100$ kazanma \u015fans\u0131n\u0131n %5, 0$ kazanma \u015fans\u0131n\u0131n %50 ve 20$ kaybetme \u015fans\u0131n\u0131n %45 oldu\u011funu varsayal\u0131m.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-21782 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/attendre13.png\" alt=\"\" width=\"235\" height=\"126\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Kazan\u00e7lar\u0131n beklenen de\u011ferini \u015fu \u015fekilde hesaplayabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Beklenen de\u011fer = 0,05*100$ + 0,5*0$ + 0,45*(-20$) = <strong>-4$<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu, e\u011fer bu oyunu sonsuz say\u0131da oynarsak, her oynad\u0131\u011f\u0131m\u0131zda ortalama 4$ kaybetmeyi bekleyece\u011fimiz anlam\u0131na gelir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 4: \u0130\u015fletme<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Beklenen de\u011fer genellikle i\u015fletmeler taraf\u0131ndan reklam harcamalar\u0131ndan beklenen getiriyi hesaplamak i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, belirli bir reklam i\u00e7in %10 olas\u0131l\u0131kla 5 ABD Dolar\u0131, %30 olas\u0131l\u0131kla 2 ABD Dolar\u0131 ve %60 olas\u0131l\u0131kla -8 ABD Dolar\u0131 getiri elde edilece\u011fini varsayal\u0131m.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-21783 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/attendre14.png\" alt=\"\" width=\"228\" height=\"126\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Reklam\u0131n beklenen de\u011ferini \u015fu \u015fekilde hesaplar\u0131z:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Beklenen de\u011fer = 0,1*5$ + 0,3*2$ + 0,6*(-8$) = <strong>-3,70$<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu \u00f6zel reklam\u0131n beklenen de\u011feri negatiftir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu, \u015firketin s\u00f6z konusu reklam\u0131 sonsuz say\u0131da kullanmas\u0131 durumunda her seferinde ortalama 3,70 ABD dolar\u0131 kaybetmeyi bekleyece\u011fi anlam\u0131na geliyor.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 5: Giri\u015fimcilik<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Beklenen de\u011fer genellikle bireyler taraf\u0131ndan giri\u015fimcili\u011fi s\u00fcrd\u00fcr\u00fcp s\u00fcrd\u00fcrmemeye karar vermek i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, bir ki\u015finin i\u015finden ayr\u0131l\u0131p serbest meslek sahibi olmas\u0131 durumunda, ilk y\u0131l\u0131nda %60 ihtimalle 20.000 $ kazanma \u015fans\u0131na, %30 ihtimalle 60.000 $ kazanma \u015fans\u0131na ve %10 20.000 $ kazanma \u015fans\u0131na sahip oldu\u011funa inand\u0131\u011f\u0131n\u0131 varsayal\u0131m. 0$.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-21785 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/attendre15.png\" alt=\"\" width=\"229\" height=\"125\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Giri\u015fimcili\u011fin ilk y\u0131l\u0131ndaki gelirlerinin beklenen de\u011ferini \u015fu \u015fekilde hesaplayabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Beklenen de\u011fer = 0,6*20.000$ + 0,3*60.000$ + 0,1*00 = <strong>30.000$<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><span style=\"color: #000000;\">Bu para miktar\u0131n\u0131n yeterli olup olmad\u0131\u011f\u0131na ba\u011fl\u0131 olarak ki\u015fi mevcut i\u015fini s\u00fcrd\u00fcrmeyi veya i\u015ften ayr\u0131lmay\u0131 se\u00e7ebilir.<\/span><\/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 beklenen de\u011fer hakk\u0131nda ek bilgi sa\u011flar:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/beklenen-deger-excel\/\" target=\"_blank\" rel=\"noopener\">Excel&#8217;de Beklenen De\u011fer Nas\u0131l Hesaplan\u0131r?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/r-cinsinden-beklenen-deger\/\" target=\"_blank\" rel=\"noopener\">R&#8217;de Beklenen De\u011fer Nas\u0131l Hesaplan\u0131r (\u00d6rneklerle)<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/ortalamaya-kiyasla-beklenen-deger\/\" target=\"_blank\" rel=\"noopener\">Beklenen de\u011fer ve ortalama: fark nedir?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Beklenen de\u011fer, bir rastgele de\u011fi\u015fkenin sonsuz say\u0131da denemede alaca\u011f\u0131 beklenen ortalamay\u0131 bize s\u00f6yleyen bir de\u011ferdir. Bir olay\u0131n beklenen de\u011ferini hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullan\u0131r\u0131z: Beklenen de\u011fer = \u03a3x * P(x) Alt\u0131n: x : veri de\u011feri P(x) : De\u011fer olas\u0131l\u0131\u011f\u0131 Bu form\u00fcl biraz kafa kar\u0131\u015ft\u0131r\u0131c\u0131 g\u00f6r\u00fcnebilir ancak ger\u00e7ek d\u00fcnyadaki \u00f6rnekler ba\u011flam\u0131nda kullan\u0131ld\u0131\u011f\u0131n\u0131 g\u00f6rd\u00fc\u011f\u00fcn\u00fczde daha anlaml\u0131 olacakt\u0131r. [&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-2426","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>Ger\u00e7ek Hayatta Beklenen De\u011ferin Hesaplanmas\u0131na 5 \u00d6rnek - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, ger\u00e7ek d\u00fcnyadaki durumlarda beklenen de\u011ferin hesaplanmas\u0131na ili\u015fkin \u00e7e\u015fitli \u00f6rnekler sunulmaktad\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-gercek-ornekler\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Ger\u00e7ek Hayatta Beklenen De\u011ferin Hesaplanmas\u0131na 5 \u00d6rnek - 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