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The joint density function of X and Y is given

The joint density function of X and Y is given by

f (x, y) = xe−x(y+1) x > 0, y > 0

(a) Find the conditional density of X, given Y = y, and that of Y, given X = x.

(b) Find the density function of Z = XY.

f (x, y) = xe−x(y+1) x > 0, y > 0

(a) Find the conditional density of X, given Y = y, and that of Y, given X = x.

(b) Find the density function of Z = XY.

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