{"id":82,"date":"2023-08-05T16:44:39","date_gmt":"2023-08-05T16:44:39","guid":{"rendered":"https:\/\/statorials.org\/tr\/matematiksel-beklenti-veya-beklenen-deger\/"},"modified":"2023-08-05T16:44:39","modified_gmt":"2023-08-05T16:44:39","slug":"matematiksel-beklenti-veya-beklenen-deger","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/matematiksel-beklenti-veya-beklenen-deger\/","title":{"rendered":"Matematiksel beklenti (veya beklenen de\u011fer)"},"content":{"rendered":"<p>Bu makalede, bir rastgele de\u011fi\u015fkenin matematiksel beklentisinin (veya beklenen de\u011ferinin) ne oldu\u011fu ve bunun nas\u0131l hesaplanaca\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. Matematiksel umudun \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmas\u0131n\u0131 bulacaks\u0131n\u0131z. Ek olarak, herhangi bir veri k\u00fcmesinin beklenen de\u011ferini \u00e7evrimi\u00e7i bir hesap makinesiyle bulabilirsiniz. <\/p>\n<h2 class=\"wp-block-heading\" id=\"que-es-la-esperanza-matematica-o-valor-esperado\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-esperanza-matematica-o-valor-esperado\"><\/span> Matematiksel beklenti (veya beklenen de\u011fer) nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0130statistikte <strong>beklenen de\u011fer<\/strong> olarak da adland\u0131r\u0131lan <strong>beklenti<\/strong> , bir rastgele de\u011fi\u015fkenin ortalama de\u011ferini temsil eden bir say\u0131d\u0131r. Matematiksel beklenti, rastgele olaylar\u0131n de\u011ferlerinden ve bunlar\u0131n meydana gelme olas\u0131l\u0131klar\u0131ndan olu\u015fan t\u00fcm \u00fcr\u00fcnlerin toplam\u0131na e\u015fittir.<\/p>\n<p> Beklenti sembol\u00fc b\u00fcy\u00fck E&#8217;dir, \u00f6rne\u011fin X istatistiksel de\u011fi\u015fkeninin beklentisi E(X) ile temsil edilir.<\/p>\n<p> Benzer \u015fekilde bir veri setinin matematiksel beklenti de\u011feri de onun ortalamas\u0131 (n\u00fcfus ortalamas\u0131) ile \u00f6rt\u00fc\u015fmektedir. <\/p>\n<h2 class=\"wp-block-heading\" id=\"como-calcular-la-esperanza-matematica\"><span class=\"ez-toc-section\" id=\"como-calcular-la-esperanza-matematica\"><\/span> Matematiksel beklenti nas\u0131l hesaplan\u0131r?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ayr\u0131k bir de\u011fi\u015fkenin matematiksel beklentisini hesaplamak i\u00e7in a\u015fa\u011f\u0131daki ad\u0131mlar izlenmelidir:<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">Her olas\u0131 olay\u0131, ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131yla \u00e7arp\u0131n.<\/span><\/li>\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">\u00d6nceki ad\u0131mda elde edilen t\u00fcm sonu\u00e7lar\u0131 toplay\u0131n.<\/span><\/li>\n<li> <span style=\"color:#101010;font-weight: normal;\">Elde edilen de\u011fer, de\u011fi\u015fkenin matematiksel beklentisidir (veya beklenen de\u011feridir).<\/span><\/li>\n<\/ol>\n<p> Dolay\u0131s\u0131yla, <strong>ayr\u0131 bir de\u011fi\u015fkenin matematiksel beklentisini (veya beklenen de\u011ferini) hesaplama form\u00fcl\u00fc<\/strong> a\u015fa\u011f\u0131daki gibidir: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/espoir-mathematiques-valeur-attendue.png\" alt=\"matematiksel beklenti veya beklenen de\u011fer\" class=\"wp-image-1752\" width=\"279\" height=\"279\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \ud83d\udc49Herhangi <u style=\"text-decoration-color:#FF8A05;\">bir veri setinin beklenen de\u011ferini hesaplamak i\u00e7in a\u015fa\u011f\u0131daki hesaplay\u0131c\u0131y\u0131 kullanabilirsiniz.<\/u><\/p>\n<p> Yukar\u0131daki form\u00fcl\u00fcn yaln\u0131zca rastgele de\u011fi\u015fkenin ayr\u0131k olmas\u0131 durumunda (\u00e7o\u011fu durumda) kullan\u0131labilece\u011fini unutmay\u0131n. Ancak de\u011fi\u015fken s\u00fcrekli ise matematiksel beklentiyi elde etmek i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanmam\u0131z gerekir:<\/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-c0ecbcb5a0ab0deb8d097268ac2911f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle E(X)=\\int_\\mathbb{R} x\\cdot f_x(x) dx \" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"174\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Alt\u0131n<\/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-f27dd617611a2ded87c3e79c1ee76fa3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f_x\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"17\" style=\"vertical-align: -4px;\"><\/p>\n<p> s\u00fcrekli de\u011fi\u015fkenin yo\u011funluk fonksiyonudur <\/p>\n<h2 class=\"wp-block-heading\" id=\"ejemplo-de-la-esperanza-matematica\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-esperanza-matematica\"><\/span> matematiksel beklenti \u00f6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Beklentinin (veya beklenen de\u011ferin) tan\u0131m\u0131 g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda, hesaplaman\u0131n nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131 g\u00f6rebilmeniz i\u00e7in a\u015fa\u011f\u0131da somut bir \u00f6rnek verilmi\u015ftir.<\/p>\n<ul>\n<li> Bir ki\u015fi, zar at\u0131ld\u0131\u011f\u0131nda ortaya \u00e7\u0131kan say\u0131ya g\u00f6re para kazanabilece\u011fi veya kaybedebilece\u011fi bir oyuna kat\u0131l\u0131r. 1 at\u0131\u015fta 800 $ kazan\u0131rs\u0131n\u0131z, 2 veya 3 at\u0131\u015fta 500 $ kaybedersiniz ve 4, 5 veya 6 at\u0131\u015fta 100 $ kazan\u0131rs\u0131n\u0131z. Kat\u0131l\u0131m \u00fccreti 50$&#8217;d\u0131r. Bu olas\u0131l\u0131k oyununa kat\u0131lmay\u0131 tavsiye eder misiniz?<\/li>\n<\/ul>\n<p> Yap\u0131lacak ilk \u015fey, her olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 belirlemektir. Zar\u0131n alt\u0131 y\u00fcz\u00fc oldu\u011fundan herhangi bir say\u0131 gelme olas\u0131l\u0131\u011f\u0131:<\/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-b6f7689a151fef994183ad359ae578b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p(\\text{obtener un n\\'umero})=\\cfrac{1}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"206\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Dolay\u0131s\u0131yla her bir olay\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131: <\/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-3ad9bd3479cfff0fd8a669549b972ecb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p(\\text{ganar }\\$800)=\\cfrac{1}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"143\" style=\"vertical-align: -12px;\"><\/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-cc814922859e0fd0be7476101a6decc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p(\\text{perder }\\$500)=2\\cdot \\cfrac{1}{6}=\\cfrac{2}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"206\" style=\"vertical-align: -12px;\"><\/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-b2a717f65fcc37f0ec7e338271bef523_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p(\\text{ganar }\\$100)=3\\cdot \\cfrac{1}{6}=\\cfrac{3}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"199\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Art\u0131k her olay\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131n\u0131 bildi\u011fimize g\u00f6re beklenti i\u00e7in matematiksel form\u00fcl\u00fc uyguluyoruz:<\/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-2634d90a3d741a7681987d3e7f45ebd1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle E(X)=\\sum_{i=1}^nx_i\\cdot p_i\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"139\" style=\"vertical-align: -21px;\"><\/p>\n<\/p>\n<p> Ve matematiksel beklentiyi (veya beklenen de\u011feri) hesapl\u0131yoruz:<\/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-3a7532f7bc4f9a6fc9c367fe2e28d0bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E(X)=800\\cdot\\cfrac{1}{6}-500\\cdot \\cfrac{2}{6}+100\\cdot\\cfrac{3}{6}=\\$16,67\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"338\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Beklenen de\u011fer, bu oyuna kat\u0131lman\u0131n bedelinden daha d\u00fc\u015f\u00fckt\u00fcr, bu nedenle oynamamak daha iyi olur \u00e7\u00fcnk\u00fc uzun vadede para kaybedersiniz. Sadece 1&#8217;e ula\u015ft\u0131\u011f\u0131nda kat\u0131l\u0131rsan\u0131z b\u00fcy\u00fck bir k\u00e2r elde edebilirsiniz, ancak uzun vadede zarar etme olas\u0131l\u0131\u011f\u0131n\u0131z y\u00fcksektir.<\/p>\n<p> Matematiksel beklenti sonucunun bazen imkans\u0131z bir de\u011fer olabilece\u011fini, \u00f6rne\u011fin bu durumda 16,67$&#8217;\u0131n elde edilemeyece\u011fini belirtmek gerekir. <\/p>\n<h2 class=\"wp-block-heading\" id=\"calculadora-de-la-esperanza-matematica\"><span class=\"ez-toc-section\" id=\"calculadora-de-la-esperanza-matematica\"><\/span> Beklenti hesaplay\u0131c\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Beklenen de\u011feri hesaplamak i\u00e7in a\u015fa\u011f\u0131daki hesap makinesine bir dizi istatistiksel veri girin. \u0130lk kutuya her olay\u0131n de\u011ferini, ikinci kutuya ise ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131n\u0131 ayn\u0131 s\u0131rayla yazmal\u0131s\u0131n\u0131z.<\/p>\n<p> Veriler bir bo\u015flukla ayr\u0131lmal\u0131 ve ondal\u0131k ay\u0131r\u0131c\u0131 olarak nokta kullan\u0131larak girilmelidir.<\/p>\n<form action=\"\" method=\"post\">\n<ul>\n<li> Her olay\u0131n de\u011feri: <\/li>\n<\/ul>\n<p><textarea name=\"datosX\" style=\"border:1.5px solid #4FC3F7; border-radius:15px;\" placeholder=\"3 4 1 7 5 ...\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce los valores de los sucesos aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/textarea><\/p>\n<ul style=\"margin-top:25px\">\n<li> Her olay\u0131n olas\u0131l\u0131\u011f\u0131: <\/li>\n<\/ul>\n<p><textarea name=\"datosP\" style=\"border:1.5px solid #4FC3F7; border-radius:15px;\" placeholder=\"0.1 0.25 0.4 0.05 0.15 ...\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce las probabilidades aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/textarea><\/p>\n<div style=\"text-align:center\"><input align=\"center\" style=\"border-radius:30px; margin: 20px\" type=\"submit\" name=\"submit\" value=\"Matematiksel beklentiyi hesaplay\u0131n\"><\/div>\n<\/form>\n<h2 class=\"wp-block-heading\" id=\"propiedades-de-la-esperanza-matematica\"><span class=\"ez-toc-section\" id=\"propiedades-de-la-esperanza-matematica\"><\/span> Matematiksel beklentinin \u00f6zellikleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Matematiksel beklentinin \u00f6zellikleri a\u015fa\u011f\u0131daki gibidir:<\/p>\n<ul>\n<li> Bir sabitin matematiksel beklentisi kendisidir.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-564923a9300f678924c2bf5d02fb5821_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E(k)=k\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Bir rastgele de\u011fi\u015fkenin bir skalerle \u00e7arp\u0131m\u0131 beklentisi, bu de\u011fi\u015fkenin beklentisinin bu skalerle \u00e7arp\u0131m\u0131na e\u015fittir.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-506787cf97f31936eef0579d1471a5bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E(k\\cdot X)=k\\cdot E(X)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"156\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> \u0130ki de\u011fi\u015fkenin toplam\u0131n\u0131n matematiksel beklentisi, her bir de\u011fi\u015fkenin matematiksel beklentilerinin toplam\u0131na e\u015fittir.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-3cfd9f255e02675ec64ec472d0c997c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E(X+Y)=E(X)+E(Y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"210\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Genel olarak iki de\u011fi\u015fkenin \u00e7arp\u0131lmas\u0131 farkl\u0131 bir matematiksel beklenti \u00fcretir. Sonu\u00e7 yaln\u0131zca de\u011fi\u015fkenler ba\u011f\u0131ms\u0131zsa ayn\u0131d\u0131r.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-116cfab17848d8aa4a3833600bd3215a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E(X\\cdot Y)\\neq E(X)\\cdot E(Y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"193\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Bir de\u011fi\u015fkenin t\u00fcm de\u011ferleri s\u0131f\u0131rdan b\u00fcy\u00fck veya s\u0131f\u0131ra e\u015fitse o de\u011fi\u015fkenin matematiksel beklentisi de pozitif veya s\u0131f\u0131ra e\u015fittir.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-4830aa6f68f621f7bac3ffa0b2d8d2db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\geq 0 \\ \\longrightarrow \\ E(X)\\geq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"175\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Bir de\u011fi\u015fkenin t\u00fcm de\u011ferleri di\u011fer de\u011fi\u015fkenin t\u00fcm de\u011ferlerinden k\u00fc\u00e7\u00fckse iki de\u011fi\u015fkenin beklentileri de ayn\u0131 ili\u015fkiye sahiptir.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f236222136aa7e5cab6ff999cfbecb9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\leq Y \\ \\longrightarrow \\ E(X)\\leq E(Y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"213\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Bir de\u011fi\u015fkenin iki de\u011ferle s\u0131n\u0131rl\u0131 oldu\u011funu biliyorsak, onun matematiksel beklentisi de mant\u0131ksal olarak s\u0131n\u0131rl\u0131d\u0131r. <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f1241572e77188af4dbd932f7415c0dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\n\n<ul>\n<li> Si une variable est la combinaison lin\u00e9aire d&#8217;une autre variable, ses attentes math\u00e9matiques satisfont \u00e0 la m\u00eame relation alg\u00e9brique : <\/li>\n<\/ul>\n<p>[latex]Y=a+bX \\ \\longrightarrow \\ E(Y)=a+b\\cdot E(X)&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;41&#8243; width=&#8221;1116&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\" id=\"para-que-sirve-la-esperanza-matematica\"><span class=\"ez-toc-section\" id=\"%c2%bfpara-que-sirve-la-esperanza-matematica\"><\/span> Matematiksel beklenti ne i\u00e7in kullan\u0131l\u0131r?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bu son b\u00f6l\u00fcmde matematiksel umudun anlam\u0131n\u0131 daha derinlemesine inceleyece\u011fiz. Somut olarak bu istatistiksel \u00f6l\u00e7\u00fcn\u00fcn ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131n\u0131 g\u00f6rece\u011fiz ve b\u00f6ylece kavram\u0131 daha iyi anlayaca\u011f\u0131z.<\/p>\n<p> Matematiksel beklenti (veya beklenen de\u011fer), olas\u0131l\u0131ksal bir uzayda uzun vadede kazan\u0131lmas\u0131 veya kaybedilmesi beklenen miktar\u0131n de\u011ferini elde etmek i\u00e7in kullan\u0131l\u0131r. Bir ba\u015fka deyi\u015fle matematiksel beklenti uzun vadede elde edilecek getiriyi ifade etmektedir.<\/p>\n<p> Bir ki\u015fi bir \u015firketin hisselerini sat\u0131n almak gibi bir yat\u0131r\u0131m yapmay\u0131 d\u00fc\u015f\u00fcnd\u00fc\u011f\u00fcnde dikkate al\u0131nmas\u0131 gereken parametrelerden biri matematiksel beklentidir. \u00c7\u00fcnk\u00fc bu yat\u0131r\u0131m\u0131 birka\u00e7 kez yapsan\u0131z elde edece\u011finiz ekonomik getiri matematiksel beklentinin de\u011feri kadar olacakt\u0131r. Elde edilen faydalar\u0131n ortalamas\u0131 olarak kabul edilebilir.<\/p>\n<p> Benzer \u015fekilde, matematiksel beklenti ekonometri, kuantum fizi\u011fi, ticaret ve hatta biyoloji gibi di\u011fer alanlarda da kullan\u0131lmaktad\u0131r.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede, bir rastgele de\u011fi\u015fkenin matematiksel beklentisinin (veya beklenen de\u011ferinin) ne oldu\u011fu ve bunun nas\u0131l hesaplanaca\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. Matematiksel umudun \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmas\u0131n\u0131 bulacaks\u0131n\u0131z. Ek olarak, herhangi bir veri k\u00fcmesinin beklenen de\u011ferini \u00e7evrimi\u00e7i bir hesap makinesiyle bulabilirsiniz. Matematiksel beklenti (veya beklenen de\u011fer) nedir? \u0130statistikte beklenen de\u011fer olarak da adland\u0131r\u0131lan beklenti , bir rastgele de\u011fi\u015fkenin ortalama de\u011ferini [&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-82","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 Matematiksel beklenti (veya beklenen de\u011fer)<\/title>\n<meta name=\"description\" content=\"Bu makalede, bir rastgele de\u011fi\u015fkenin matematiksel beklentisinin (veya beklenen de\u011ferinin) ne oldu\u011fu ve nas\u0131l hesaplanaca\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. Matematiksel umudun \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmas\u0131n\u0131 bulacaks\u0131n\u0131z. Ek olarak, \u00e7evrimi\u00e7i bir hesap makinesiyle herhangi bir veri k\u00fcmesinin beklenen de\u011ferini bulabilirsiniz.\" \/>\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\/matematiksel-beklenti-veya-beklenen-deger\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Matematiksel beklenti (veya beklenen de\u011fer)\" \/>\n<meta property=\"og:description\" content=\"Bu makalede, bir rastgele de\u011fi\u015fkenin matematiksel beklentisinin (veya beklenen de\u011ferinin) ne oldu\u011fu ve nas\u0131l hesaplanaca\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. Matematiksel umudun \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmas\u0131n\u0131 bulacaks\u0131n\u0131z. Ek olarak, \u00e7evrimi\u00e7i bir hesap makinesiyle herhangi bir veri k\u00fcmesinin beklenen de\u011ferini bulabilirsiniz.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/matematiksel-beklenti-veya-beklenen-deger\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-05T16:44:39+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/espoir-mathematiques-valeur-attendue.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=\"5 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/matematiksel-beklenti-veya-beklenen-deger\/\",\"url\":\"https:\/\/statorials.org\/tr\/matematiksel-beklenti-veya-beklenen-deger\/\",\"name\":\"\u25b7 Matematiksel beklenti (veya beklenen de\u011fer)\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-08-05T16:44:39+00:00\",\"dateModified\":\"2023-08-05T16:44:39+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Bu makalede, bir rastgele de\u011fi\u015fkenin matematiksel beklentisinin (veya beklenen de\u011ferinin) ne oldu\u011fu ve nas\u0131l hesaplanaca\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. 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