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Problem 2 (18 points) Let X and Y be independent standard normal random variables N(0, 1), and let U = + (X+Y) and W =-

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Problem 2 (18 points) Let X and Y be independent standard normal random variables N(0, 1), and let U = + (X+Y) and W =- V ( X - Y ) . (a) Find the joint pdf of (U, W). (b) Find the marginal pdf of U and W. (c) Find the pdf of W2 and write down its name of distribution. (d) Find Cov(XY, Y) and E(W4)

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