Question: 18. Let a, b > 0. Independent positive random variables X and Y have probability densities 1 (a) xa1ex , 1 (b) yb1ey , for

18. Let

a, b > 0. Independent positive random variables X and Y have probability densities 1

Ŵ(a)

xa−1e−x , 1

Ŵ(b)

yb−1e−y , for x, y ≥ 0, respectively, and U and V are defined by U = X + Y, V =

X X + Y

.

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