Question: Let X and Y be independent normally distributed random variables Problem 1: a) Let X and Y be independent normally distributed random variables ~ N(0,02),

Let X and Y be independent normally distributed random variables

Problem 1: a) Let X and Y be independent normally distributed random variables ~ N(0,02), determine if U and V (defined below) are independent random variables. U = X2 - Y2 XY VX2 + 12 and V = VX2 + 12 b) X and W are independent n and m - dimensional Gaussion random vectors with X ~ N(m,Z), W ~ N(0,Q) and Y = CX + W, YER", m <.>

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