Let X have a uniform distribution U(0, 2), and let the conditional distribution of Y, given that X = x, be U(0, x 2 ). (a) Determine f (x, y), the...

Let X have a uniform distribution U(0, 2), and let the conditional distribution of Y, given that X = x, be U(0, x2).

(a) Determine f (x, y), the joint pdf of X and Y.

(b) Calculate fY(y), the marginal pdf of Y.

(c) Compute E(X | y), the conditional mean of X, given that Y = y.

(d) Find E(Y | x), the conditional mean of Y, given that X = x.