You are developing a strategy for investing in two different shares. The anticipated annual return for a $$1,000$ investment in each share has the following probability distribution: Returns Probability $0\mathrm{.}10\mathrm{.}30\mathrm{.}3$ Share X Share Y $-$$$100080150$ $$50150-200\mathrm{.}3-10018$

a$.$ Calculate: i$.$ the expected return for share X and for share Y ii$.$ the standard deviation for share X and for share Y iii. the covariance of share X and share Y

b$.$ Would you invest in share X or share Y$?$ Explain. Suppose that you wanted to create a portfolio that consists of share X and share Y$.$

c$.$ Calculate the portfolio expected return and portfolio risk for each of the following percentages invested in share X: i$.30\%$ ii$.50\%$ iii. $70\%18/54$

d$.$ On the basis of the results of your calculations in part $($c$),$ which portfolio would you recommend? Explain