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U Question 3 (15 points = 5 + 5 + 5). Suppose that the random variable X ~ N(0, 02), and consider a new random variable Y obtained through the exponential transformation, Y = ex . a) Show that the CDF of Y is given by Fy (y) = $ In y where (z) is CDF of the standard normal random variable. b) For o = 2, compute P(1 0, fy(y) = V2Toy otherwise