$1.$ 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.

Scenario Probability Stock X returns $($in $\%)$ Stock Y returns $($in $\%)$

Boom $0\mathrm{.}252030$

Normal $0\mathrm{.}5610$

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.