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Unformatted text preview: 2. Let X, Y and Z be random variables. Consider the conditional density (10) (a) Find f(x * z) and state its support. (10) (b) Find f(y * x, z) and state its support. 3. Consider two random variables X and Y such that X -U(0, 1) and Y * X = x -N(x, x 2 ). Find: (10) (a) E(Y) (10) (b) Var(Y) (10) (c) Cov(X, Y) 2 4. Suppose the random variable Y has pfd (15) (a) Find E(Y). (15) (b) Find Var(Y). (10) 5. Suppose X 1 and X 2 are independent standard normal random variables. What is the distribution of Y = (X 1- X 2 ) 2 /2 ?...
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- Fall '10