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The joint pdf of two random variables X and Y is given by f X,Y (x, y) = y e x / y e y

The joint pdf of two random variables X and Y is given by

fX,Y (x, y) =yex/yey for x > 1 and y > 0

(a) Compute fX|Y (x|y), the conditional pdf of X given Y = y.

(b) Compute E[X2|Y = y].

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