(b) Consider two random variables, X and Y. They both take the values -1,0 and 1. The joint probabilities for each pair of values, (x, y), are given in the following table. X= -1 X=0 X=1 Y = 1 0.09 0.16 0.15 Y = 0 0.09 0.08 0.03 Y =1 0.12 0.16 0.12 i. Determine the marginal distributions and calculate the expected values Xand Y , respectively. ii. Calculate the covariance of the random variables X and Y . ii. Calculate E(X|Y =0)andE(X|X+Y =1). iv. |DefineU =|X|andV =Y. CalculateE(U)andthecovarianceofU andV. Are U and V correlated?

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