Question: Suppose that the joint probability distribution of X and Y is given by the following table.
(a) Are X and Y independent? Explain.
(b) Find the marginal distributions of X and Y.
(c) Find the conditional distribution of Y given X = 1 and hence E(Y|X = 1) and vart (Y|X = 1).
(d) Repeat part (c) for X = 2 and X = 3 and hence verify the result that V( Y) = EV( Y I X) + VE(Y|X) that is the variance of a random variable is equal to the expectation of its conditional variance plus the variance of its conditional expectation.