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6. (7 points) The conditional PDF of X given Y is (x - y)2 fxy (xly) = exp 2 and Y is a uniform random

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6. (7 points) The conditional PDF of X given Y is (x - y)2 fxy (xly) = exp 2 and Y is a uniform random variable in [0, 1). (a) Find the marginal PDF of X. (You can keep your answer in integral form) (b) Find E[X|Y] and EX' |Y]. (c) Find E[X] and Var( X)

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