Q. If \ud835\udc4b and \ud835\udc4c are random variables such that \ud835\udc38[2\ud835\udc4b + \ud835\udc4c] = 0 and \ud835\udc38[\ud835\udc4b + 2\ud835\udc4c] = 33, then \ud835\udc38[\ud835\udc4b] + \ud835\udc38[\ud835\udc4c] =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 .<\/p>\n\n\n\n
Ans:11<\/p>\n\n\n\n
Solution:<\/p>\n\n\n\n
E[x + y] = E[x] + E[y] <\/p>\n\n\n\n
E [Ax] = A E[x] <\/p>\n\n\n\n
Where E [x] represents the expected or mean value of the random variable ‘x’ <\/p>\n\n\n\n
Application: <\/p>\n\n\n\n
E[2x + y] = 0 <\/p>\n\n\n\n
2E[x] + E[y] = 0\u00a0 \u00a0\u00a0—-(1) <\/p>\n\n\n\n
E[x + 2y] = 33 <\/p>\n\n\n\n
E[x] + 2E[y] = 33\u00a0\u00a0\u00a0\u00a0—-(2) <\/p>\n\n\n\n
Adding (1) and (2) <\/p>\n\n\n\n
3E[x] + 3E[y] = 33 <\/p>\n\n\n\n
E[X] + E[Y] = 11<\/p>\n","protected":false},"excerpt":{"rendered":"
Q. If \ud835\udc4b and \ud835\udc4c are random variables such that \ud835\udc38[2\ud835\udc4b + \ud835\udc4c] = 0 and \ud835\udc38[\ud835\udc4b + 2\ud835\udc4c] = 33, then \ud835\udc38[\ud835\udc4b] + \ud835\udc38[\ud835\udc4c] =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 . Ans:11 Solution: E[x + y] = E[x] + E[y] E [Ax] = A E[x] Where E [x] represents the expected or mean value of the random variable ‘x’ […]<\/p>\n","protected":false},"author":419,"featured_media":154524,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[5141],"tags":[5140],"class_list":["post-154523","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154523","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=154523"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154523\/revisions"}],"predecessor-version":[{"id":154525,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154523\/revisions\/154525"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/154524"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=154523"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=154523"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=154523"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}