Question 1 Parts A and B are unrelated A. Suppose you own a portfolio of two stocks - Stock A and Stock B. The number of shares you own of Stocks A and B are a and B respectively. The market value of your portfolio W = ax +BY where X and Y are prices of Stocks A and B respectively. As an investor you like high market values but dislike the risk associated with stock price volatility, which can be measured by the standard deviation of stock prices. Suppose the joint pdf of stock prices, f(x,y), has the following known characteristics: MX =$ 52.5, 0x 2= 31.25 ($)2, MY= $ 55, oy 2 = 125 ($)2, E(XY) =2946.7 1. Find the mean and variance of W given that a =5 and B -10. (4 points) 2. Consider now a different joint probability distribution of stock prices. Specifically, in this new distribution, the means and variances of X and Y are the same as before, but the correlation coefficient Oxy = - 0.944. (a) Find E(W) and var(W) in this new distribution. (3 points) (b) If you were to choose between the distributions in 1. and 2., which one would you choose and why? (1 point) B. If X and Y are two independent random variables with means 30 and 60 respectively, and variances 20 and 25 respectively, can you determine the extent to which X and Y are linearly related? If yes, what is extent or degree of linear association between X and Y ? If not, why not? Explain briefly. (2 points)