3. Suppose you have some money to investfor simplicity, $1and you are planning to put a fraction w into a stock market mutual fund and the rest, 1 - w, into a bond mutual fund. Suppose that $1 invested in a stock fund yields R after 1 year and that $1 invested in a bond fund yields R, suppose that R is random with mean 0.08 (8%) and standard deviation 0.07, and suppose that R, is random with mean 0.05 (5%) and standard deviation 0.04. The correlation between R and R, is 0.25. If you place a fraction w of your money in the stock fund and the rest, 1 - w, in the bond fund, then the return on your investment is R=wR + (1 - w)R, a. Suppose that w=0.5. Compute the mean and standard deviation of R. b. Suppose that w=0.75. Compute the mean and standard deviation of R. c. What value of w makes the mean of R as large as possible? What is the standard deviation of R for this value of w? d. (Harder) What is the value of w that minimizes the standard deviation of R? (Show using a graph, algebra, or calculus.)