Given below is a bivariate distribution for the random variables x and y. a. Compute the expected value and the variance for x and y. E(x)=E(y)=Var(x)=Var(y)= b. Develop a probability distribution for x+y (to 2 decimals). \begin{tabular}{c|c} \hlinex+y & f(x+y) \\ 130 & \\ 80 & \\ 100 & \\ \hline \end{tabular} c. Using the result of part (b), compute E(x+y) and Var(x+y). E(x+y)=Var(x+y)= 3. P. Morgan Asset Management publisties information about financial investments. Between 2002 and 2011 the expected return for the 58.500 was 5.04% with a standard deviation of 19.45% and the expected return over that same period for a Core Bonds fund was 5.78% with a standard deviation of 2.13\% (3. P. Morgan Asset Management, Guide to the Markets). The publication also reported that the correfation between the 58.500 and Core Bonds is - 0.32, You are considering portfolio investments that are composed of an S\$P 500 index fund and a Core Bonds fund. a. Using the information provided, determine the covariance between the 5&.500 and Core Bonds. Round your answer to two decimal places. If required enter negative values as negative numbers. b. Construct a portfolio that is 50% invested in an 58.500 index fund and 50% in a Core Bond fund. Let x represent the Sa. 500 and y represent the Core Bond fund. Round your answers to one decimal place. r= In percentage terms, what is the expected return and standard deviation for such a portfolio? Round your answers to two decimal places. c. Construct a portfolio that is 20% invested in an 58p500 index fund and 80% invested in a Core bond fund. Let x represent the 56p soo and y represent the Core Bond fund. Round your answers to one decimal place. r=1z+ In percentage terms, what is the expected retum and standard deviation for such a portfolio? Round your answers to two decimal places. d. Construct a portfolio that is 80% invested in an 58s.500 index fund and 20% invested in a Core bond fund. Let x represent the Ss 500 and y represent the Core Bond fund. Round your answers to one decimal place