3. The joint density of X and Y is given by $$f(x, y) = C(y - x)e^{-y}$$...

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3. The joint density of X and Y is given by

$$f(x, y) = C(y - x)e^{-y}$$

-y < x < y, 0 < y < ∞

(a) Find C.

(b) Find the density function of X.

(c) Find the density function of Y.

(d) Find E[X].

(e) Find E[Y].

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