n investor has $200 to invest. She will invest $100 in each of two investments. Let X and Y denote the returns on the investments. Assume E(X) = E(Y ) = $5, and V (X) = V (Y ) = 4. The two investments are correlated with correlation ρ = 0.5. (a) Find the covariance Cov(X, Y ) between X and Y . [2] (b) Find the mean and standard deviation of the total return S = X + Y . [2] (c) Suppose now that each of the investment follow a normal distribution with their respective mean and variance. (i) What is the distribution of S? [2] (ii) Find the likelihood that the investor loses money, that is P (S < 0)