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Let X and Y have a joint density function given by f(x; y) = 3x; 0...

Let X and Y have a joint density function given by f(x; y) = 3x; 0 <= y <= x <= 1

(a) Find P(X<2Y).

(b) Find cov(X,Y).

(c) Find P(X < 1/2 |Y = 1/3).

(d) Find P(X = 1/2|Y = 1/3).

(e) Find P(X > 1/2|Y > 1/3).

(f) Find the conditional expectation E(X|Y = y).

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