Question $3(16$ marks$)$

Consider the following information:

$\backslash$table$[[$State of Economy,Probability of State,Rate of Return if State Occurs$],[$of Economy,Stock A$,$Stock B$],[$Boom$,\mathrm{.}10,\mathrm{.}25,\mathrm{.}18],[$Growth$,\mathrm{.}20,\mathrm{.}10,\mathrm{.}20],[$Normal$,\mathrm{.}50,\mathrm{.}15,\mathrm{.}04],[$Recession$,\mathrm{.}20,-\mathrm{.}12,0]]$

$($a$)$ What are the expected return rate for Stocks A and B respectively? Show your workings and round your answer in $\%$ with $2$ decimal places.

$(4$ marks$)$

$($b$)$ What are the standard deviation for Stocks A and B respectively? Show your workings and round your answer in $\%$ with $2$ decimal places.

$(6$ marks$)$

$($c$)$ If you have $$1$ million and your goal is to create a portfolio with an expected return of $9\mathrm{.}15$ percent, how much money will you invest in Stocks A and B respectively based on your answer in part $($a$)?$

$(6$ marks$)$