Question: Random variables X and Y have g(y|X = x) = 1 2x , 0 < y < 2x and f (x) = 24x2, 0 <

Random variables X and Y have g(y|X = x) = 1 2x

, 0 < y < 2x and f (x) = 24x2, 0 <

x <

1 2

.

(a) Find the joint probability density function, f (x, y).

(b) Find g(y), the marginal density for Y.

(c) Are X and Y independent? Justify your answer.

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