5.7 Given two random variables x and y: Probability of State State of of Nature 22222 Nature Variable x Variable y I 18 0 II 5 -3 III 12 15 IV 12 6 1 (a) Calculate the mean and variance of each of these variables, and the covariance between them. (b) Suppose x and y represent the returns from two assets. Calculate the mean and variance for the following portfolios: % in x 125 100 75 50 25 0-25 % in y -25 0 25 50 75 100 125 (c) Find the portfolio that has the minimum variance. (d) Let portfolio A have 75% in x and portfolio B have 25% in x. Calculate the covariance between the two portfolios. (e) Calculate the covariance between the minimum variance portfolio and portfolio A, and the covariance between the minimum variance portfolio and portfolio B.