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The joint prob. density of X and Y is f(x,y) = c xexp(-y) for 0 y x 1, and 0 otherwise. (a) Find c. (b)

The joint prob. density of X and Y is f(x,y) = c xexp(-y) for 0 y x 1, and 0 otherwise.

(a) Find c.

(b) Find the marginal density of X.

(c) Find the marginal density of Y.

(d) Find P(Y < 1/3 | X < ).

(e) Find E(X) and E(Y).

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