Consider two random variables, X and Y. They both take the values 0, 1 and 2. The joint probabilities for each pair are given by the following table. X =0 X=1 X=2 Y = 0 0 0.125 0.125 Y =1 0.125 0 0.250 Y =2 0.125 0.250 0 (a) Calculate the marginal distributions and the expected values for X and Y, respectively. (b) Calculate the covariance of X and Y. (c) A random variable W is defined as W = X - Y. Calculate the covariance of the random variables X and W. (Hint: Cov(A, A + B) = Cov(A, A) + Cov(A, B).) (d) Calculate E(X | Y = 0) and E(X | W = 1)