s College-CUNY nd Business Department pring 2018 8 Prot. Francois de Paul Silatehom ollowing joint distribution of two random variables X and Y 10 Total 0.40 15030 12 0.50 10.20 1-0.20 Total ate E(Y) and V(Y) (2pts) X-5 ( ipt) lculate E(Y/x-5) and V(Y/X-5) (2pts) Are the variables statistically X and Y independent? (Ipt) II-(6pts) 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 S1 invested in a stock fund yields R, after one year and a $1 invested in a bond fund yields R. R, and R, are random variables with expected value of 10% and 8% respectively, and standard deviation of 4% and 2% respectively. The correlation between R, and R, is 0.70. 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 wR, (Iw)R,. The risk associated with your investment is measured by the standard deviation. what is the expected return of your investment? What is its associated risk? (2pts) a 92% return on your investment? For that same share invested in bond, what level of risk If you decide to invest 40% of your $1 in stock and the rest in bond, then b. What share of your $1 money should you invest in bond in order to expect is associated with your investment? (2pts) c. What share of your $1 money should you invest in stock mutual fund in order for your investment risk to be 3%? (you can show your work using algebra, or calculus). (2pts) III (7pts) Grades on a standardized test are known to have a mean of 1000 for students in the US. The test is administered to 453 randomly selected students from Queens College, and they obtained an average grade of 1013 and a standard deviation of 108. a. Construct a 95 % confidence interval for the true average test score for Queens College students.(1pt) b. With 5% significance level, Is there a statistical evidence that Queens College tudents perform differently than other students in the US?(1pt)