63. Let the random variables X~ N(ux, o) and Y~ N(μy, o) be jointly continuous normal random variables. Now suppose their joint pdf is 1 2πσχογ X and Y are said to have a bivariate normal distribution. f(x, y) = f(x, y) -{(²-x)² + (0-4)²} (-∞∞) (2) I(-∞,∞) (Y) (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 = e 1 2πσ.συ What must be true about k for X and Y to be independent bivariate normal random variables? e [ (x-µ x)² +k(2−µx) (Y−µy ) + ( -#Y) ² } o I(-∞,∞) (x) I(-∞,∞) (y)

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