$5\mathrm{.}52$ You are trying to develop a strategy for investing in two different stocks. The anticipated annual return for a $$1,000$ investment in each stock under four different economic conditions has the following probability distribution:

$\backslash$table$[[$Probability$,$Economic Condition,Returns$],[$Stock x$,$Stock Y$],[0\mathrm{.}1,$Recession,$-50,-100],[0\mathrm{.}3,$Slow growth,$20,50],[0\mathrm{.}4,$Moderate growth,$100,130],[0\mathrm{.}2,$Fast growth,$150,200]]$ anwer using excel

Compute the

a$.$ expected return for stock $x$ and for stock $Y.$

b$.$ standard deviation for stock $x$ and for stock $Y.$

c$.$ covariance of stock $x$ and stock $Y.$

d$.$ Would you invest in stock $x$ or stock $Y?$ Explain.