Suppose you have some money to invest-for simplicity, $1-and 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 a $1 invested in a stock fund yields rs after one year and a $1 invested in a bond fund yields rb. rs and rb are random variables with expected value of 8% and 7% respectively, and standard deviation of 7% and 4% respectively. the correlation between rs and rb 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 will be r = wrs + (1-w)rb . a. compute the mean and standard deviation of r for w = .5 and w = .75 respectively. b. what value of w makes the mean (or expected value) of r as large as possible? what is the standard deviation of r for this value of w? c. what is the value of w that minimizes the standard deviation of r? (you can show this using algebra, or calculus).