Problem $2(20$ points$).$ A pension fund manager is considering two mutual funds. The first is a stock fund, the second is a long$-$term government and corporate bond fund. The probability distribution of the risky funds is as follows:

$\backslash$table$[[,$Expected Return,Standard Deviation$],[$Stock fund $(S),0\mathrm{.}20,0\mathrm{.}30],[$Bond fund $(B),0\mathrm{.}12,0\mathrm{.}15]]$

The correlation between the fund returns is $0\mathrm{.}10.$

Please keep $4$ numbers after the decimal point in your answers.

$2.$a$.(2$ points$)$ What is the covariance between the two funds' returns?

$2.$b$.(6$ points$)$ What are the weights of the two risky funds in the minimum$-$variance portfolio.

$2.$c $(4$ points$)$ What is the expected return of the minimum variance portfolio?

$2.$d$,(8$ points$)$ What is the standard deviation of the minimum variance portfolio?