{"id":161293,"date":"2023-10-25T15:05:23","date_gmt":"2023-10-25T09:35:23","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=161293"},"modified":"2023-10-25T15:05:25","modified_gmt":"2023-10-25T09:35:25","slug":"let-x1-x2-be-two-independent-normal-random-variables-with-means-%c2%b51-%c2%b52-and-standard-deviations-s1-s2","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/let-x1-x2-be-two-independent-normal-random-variables-with-means-%c2%b51-%c2%b52-and-standard-deviations-s1-s2\/","title":{"rendered":"Let X1, X2 be two independent normal random variables with means \u00b51, \u00b52 and standard deviations s1, s2,"},"content":{"rendered":"\n<p>Q. Let <em>X<\/em>1<em>, X<\/em>2 be two independent normal random variables with means <em>\u00b51, \u00b52 <\/em>and standard deviations s1<em>, <\/em>s2<em>, <\/em>respectively. Consider <em>Y = X<\/em>1 \u2013 <em>X<\/em>2; <em>\u00b5<\/em>1 = <em>\u00b5<\/em>2 =1, s1 = 1, s2 = 2. Then,<\/p>\n\n\n\n<p>A. <em>Y <\/em>is normally distributed with mean 0 and variance 1<\/p>\n\n\n\n<p>B. <em style=\"font-size: inherit; background-color: var(--base-3); color: var(--contrast);\">Y <\/em><span style=\"font-size: inherit; background-color: var(--base-3); color: var(--contrast);\">is normally distributed with mean 0 and variance 5<\/span><\/p>\n\n\n\n<p>C. <em style=\"font-size: inherit; background-color: var(--base-3); color: var(--contrast);\">Y <\/em><span style=\"font-size: inherit; background-color: var(--base-3); color: var(--contrast);\">has mean 0 and variance 5, but is NOT normally distributed<\/span><\/p>\n\n\n\n<p>D. <em>Y <\/em>has mean 0 and variance 1, but is NOT normally distributed<\/p>\n\n\n\n<p>Ans: Y is normally distributed with mean 0 and variance 5<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Q. Let X1, X2 be two independent normal random variables with means \u00b51, \u00b52 and standard deviations s1, s2, respectively. Consider Y = X1 \u2013 X2; \u00b51 = \u00b52 =1, s1 = 1, s2 = 2. Then, A. Y is normally distributed with mean 0 and variance 1 B. Y is normally distributed with mean [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":161294,"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-161293","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\/161293","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=161293"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/161293\/revisions"}],"predecessor-version":[{"id":161295,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/161293\/revisions\/161295"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/161294"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=161293"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=161293"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=161293"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}