{"id":7019,"date":"2021-10-22T15:22:45","date_gmt":"2021-10-22T09:52:45","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7019"},"modified":"2021-10-25T09:37:36","modified_gmt":"2021-10-25T04:07:36","slug":"the-mean-and-variance-of-a-random-variable-x-having-a-binomial-distribution-are-4-and-2-respectively-then-px-1-is","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/the-mean-and-variance-of-a-random-variable-x-having-a-binomial-distribution-are-4-and-2-respectively-then-px-1-is\/","title":{"rendered":"The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, then P(X = 1) is"},"content":{"rendered":"

Solution :<\/h2>\n

Given that, for binomial distribution mean, np = 4 and variance, npq = 2.<\/p>\n

\\(\\therefore\\)\u00a0 q = 1\/2, but p + q = 1 \\(\\implies\\) p = 1\/2<\/p>\n

and n \\(\\times\\) \\(1\\over 2\\) = 4 \\(\\implies\\) n = 8<\/p>\n

We know that,\u00a0 P(X = r) = \\(^nC_r p^r q^{n-r}\\)<\/p>\n

\\(\\therefore\\)\u00a0 P(X = 1) = \\(^8C_1\\)\\(({1\\over 2})^7\\)\\(({1\\over 2})^1\\)<\/p>\n

= 1\/32<\/p>\n

\n

Similar Questions<\/h3>\n

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The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observation of the set is increased by 2, then the median of the new is<\/a><\/p>\n

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Solution : Given that, for binomial distribution mean, np = 4 and variance, npq = 2. \\(\\therefore\\)\u00a0 q = 1\/2, but p + q = 1 \\(\\implies\\) p = 1\/2 and n \\(\\times\\) \\(1\\over 2\\) = 4 \\(\\implies\\) n = 8 We know that,\u00a0 P(X = r) = \\(^nC_r p^r q^{n-r}\\) \\(\\therefore\\)\u00a0 P(X = 1) …<\/p>\n

The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, then P(X = 1) is<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,58],"tags":[],"yoast_head":"\nThe mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, then P(X = 1) is<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/the-mean-and-variance-of-a-random-variable-x-having-a-binomial-distribution-are-4-and-2-respectively-then-px-1-is\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, then P(X = 1) is\" \/>\n<meta property=\"og:description\" content=\"Solution : Given that, for binomial distribution mean, np = 4 and variance, npq = 2. 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