Suppose there are three states of the economy: boom, moderate growth and reces$-$

sion. The annual returns for GM and Ford stocks in each economic state is given in

the table below.

The probabilties of the three states are $0\mathrm{.}5$ for Recession and $0\mathrm{.}25$ each for the other

two. If we define $x$ as the return from GM $($in $\%),$ the p$.$m$.$f of $x$ is as follows.

$($a$)$ Calculate the mean and standard deviation of the return for both GM and

Ford.

$($b$)$ Compare the expected returns and risk between the two stock options.

$($c$)$ You have invested $25\%$ of your money in GM and $75\%$ in Ford. What is the

mean of your portfolio's return?