$17)$ Investment Portfolio AnalysisA portfolio manager is analyzing two stocks, Stock A and Stock B$.$ The manager has compiled the following historical data on the monthly returns of each stock: Stock A: Expected monthly return E$($RA$)=8\%$E$($R$\_$A$)=8\backslash \%$E$($RA$)=8\%,$ with a standarddeviation oA$=5\%\backslash$sigma$\_$A $=5\backslash \%$aA$=5\%.$ Stock B: Expected monthly return E$($RB$)=12\%$E$($R$\_$B$)=12\backslash \%$E$($RB$)=12\%,$ with a standard deviation oB$=7\%|$sigma$\_$B $=7\backslash \%$oB$=7\%.$ The correlation coefficient between the returns of Stock A and Stock B ispAB$=0\mathrm{.}3\backslash$rho$\_\{$AB$\}=0\mathrm{.}3$pAB$=0\mathrm{.}3.$The manager plans to allocate $60\%$ of the portfolio to Stock A and $40\%$ to Stock B$.($a$)$ What is the expected return of the portfolio?$($b$)$ What is the standard deviation of the portfolio?$($c$)$ What is the probability that the portfolio will return less than $0\%$ in a given month, assuming the portfolio returns are normally distributed?