Problem 2 The following covariance matrix for X1 and X; must be wrong. Why? X1 X2 X1 25 60 X2 60 100 Problem 3 The joint distribution of the changes in Viacom (V) and Walmart (W1 stock prices one month from now is given here: V=v W=w PlV=v,W=w| -0.05 -0.05 0.1 0 0 0.3 0.10 0.10 0.1 0.10 0.15 0.1 0.30 0.10 0.2 0.30 0.15 02 For example, the first row indicates that the joint probability of Viacom stock going down by $0.05 and Walmart stock going down by $0.05 is 0.1. You may assume that PlV = v, W = w) is zero for any combination of V and W values not shown in the table. Hint: It may be easier to answer the questions if you create the following table. (You fill in the numbers.) W 0.05 0 0.1 0.15 -0.05 V 0 0.1 0.3 3] What are the marginal distributions ofV and W? Present the marginal distributions for each random variable separately in a table format. For example, the marginal distribution of V should look like the table below. (You fill in the numbers.) V=v PlV=vJ b] Find the following probabilities. Show your work to receive full credit. 1] PW 50.10 | w z 0) 2] PlVSOand W 0.15 I W = 0.10) cl Find the correlation between V and W, Show your work to receive full credit. To cut down the tedious calculations. lam giving you the following: SD(W) = 0.07, SDlV) = 0.14, and Cov(V,W] = 0.0083. d] Let X = 100V 50W. X represents the total change for a portfolio consisting of 100 shares ofViacom and 50 shares of Walmart shorted. Find E[X] and SDlX). Show your work to receive full credit. 2) Let Y = 100V + nW, Y represents the change for a portfolio consisting of 100 shares of Viacom and n shares of Walmart. Here, n could be a negative integer which means you are shorting Walmart. How many shares of Walmart should you buy or short to make the variance [or equivalently the SD] in your portfolio Y as small as possible? What is the value of the minimum 50? Show your work to receive full credit. Hint: You can use calculus or simply plot the equation for Var(Y) versus a wide range of n values to see at which value of n the minimum of Var(Y) occurs