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The continuous random variable X has pdff(:l?) = gate—3"”, a: 2 O.The conditional pdf of Y given X : 33 is given by Imam) = ate—my, y 2 0. (3.) Write down the joint pdf of X and Y.(b) Find the marginal pdf of Y.((3) Let U 2 XY, evaluate P(U > 1). (d) Find an expression for the conditional expectation E (Y|X ), and hence evaluate E (Y)