The rate of return of an asset is the change in price divided by the initial price (denoted as r). suppose that $10,000 is used to purchase shares in three stocks with rates of returns x1, x2, x3. initially, $2500, $3000, and $4500 are allocated to each one, respectively. after one year, the distribution of the rate of return for each is normally distributed with the following parameters: μ1 = 0.12, σ1 = 0.14, μ2 = 0.04, σ2 = 0.02, μ3 = 0.07, σ3 = 0.08. a. assume that these rates of return are independent. determine the mean and variance of the rate of return after one year for the entire investment of $10,000. b. assume that x1 is independent of x2 and x3 but that the covariance between x2 and x3 is −0.005. repeat part (a). c. compare the means and variances obtained in parts (a) and (b) and comment on any benefits from negative covariances between the assets.