3. There are two stocks (stock 1 and stock 2) whose annual returns are random and denoted by X and Y. The joint probability distribution of X and Y are given by: X 1% 2% 3% 1/4 0 1/4 0 O Y 1% 3% a. Compute E(X), E(Y), Var(x), and Var(Y). b. Compute Cov(X,Y). Show that X and Y are not statistically independent. c. Suppose that you are thinking about investing in either stock 1 or stock 2 or both; i.e., return on your investment portfolio will be: R = WX + (1-w). a. Show that E(R) = 2% no matter what w is. Find w that minimizes Var(R). b. Suppose that you have two investment strategies: a safe strategy and a risky strategy. In the safe strategy, you invest only in the US government treasury bonds and earn 1.5% return. Alternatively, in the risky strategy, you invest 50% of your wealth in stock 1 and the other 50% in stock 2. Let R denote return on your investment. Then, R = 1.5 in the safe strategy, whereas R = .5X + SY in the risky strategy Suppose that you choose the risky strategy. Write down the probability distribution of Rin a table. Calculate E(R). ii. Suppose that your utility function is given by: u(R) = In(R). Which investment strategy do you choose