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Let X have the gamma (4, 2) distribution. For each x > 0, let the conditional distribution of Y given X = x be uniform

Let X have the gamma (4, 2) distribution. For each x > 0, let the conditional distribution of Y given X = x be uniform on the interval (x, x). Let W = |Y |.

(a) Find E(Y ) and Var(Y ).

(b) Given X = x, what is the conditional distribution of W?

(c) Find E(W).

(d) Find V ar(W).

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