63. Let the random variables X~ N(ux, o) and Y~ N(μy, o) be jointly continuous normal randomvariables. Now suppose their joint pdf is12πσχογX and Y are said to have a bivariate normal distribution.(a) Given this joint pdf, show that X and Y are independent.(b) The most general form of the pdf for a bivariate normal distribution is(-x)® +k(-x)(y-ux)+}of(x, y)=f(x, y)-{(²-x)² + (0-1)²} (-∞∞) (¹) I(-∞,∞) (Y)ee1I(-∞,∞) (x) I(-∞,∞) (y)2πστσυWhat must be true about k for X and Y to be independent bivariate normal random variables?(v-μ)2

Answered: 63. Let the random variables X~ N(ux,…

A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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