A. Consider the following linear combination of three random variables: (aX +bY + cZ). Suppose that a = b =c=(1/3), and that the variables have equal means and variances; that is E(X)=E(Y)=E(Z)= H and var(X)=var(Y)=var(Z)=02. As well, the covariances are all the same. In particular, cov(X, Y) = cov(X, Z) = cov(Y, Z) = 62/2. Find expressions for (i) E(aX+ bY + cZ), (ii) var(aX+ bY + cZ), and (iii) the correlation coefficient Pxy. (6 points) B. Suppose you are given the following probability distribution of X: X: 1 2 3 4 5 f(x) 0.10 0.25 0.40 0.20 0.05 Find the following means: E(X) and E[g(X)] when g(X)= bX? where the constant b > 0. (4 points)