The table below reports the annual returns to stocks $x$ and $Y$ in three different scenarios. You will verify your calculations in question $2,$ so don't use a spreadsheet for this question yet.

$\backslash$table$[[$Scenario$,$Probability,Stock X returns $($in $\%),$Stock Y returns $($in $\%)],[$Boom$,0\mathrm{.}25,20,30],[$Normal$,0\mathrm{.}5,6,10],[$Bust$,0\mathrm{.}25,-15,-25]]$

a$.$ What are the expected returns for stocks $x$ and $Y$ respectively? Show your calculations.

b$.$ What are the standard deviations for stocks $x$ and $Y$ respectively? Show your calculations.

c$.$ Calculate the Sharpe ratio for each stock.