9. The joint probability density function of X and Y is given by

$$f(x, y) = \frac{6}{7} (x^2 + \frac{x}{2}y)$$

0 < x < 1, 0 < y < 2

(a) Verify that this is indeed a joint density function.

(b) Compute the density function of X.

(c) Find P{X > Y}.

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(d) Find P{Y > X < 1}.

(e) Find E[X].

(f) Find E[Y].