Consider a market consisting of only three stocks labeled A$,$ B and C$.$ In the market, there are $100$ shares of stock A sold at $$1$ per share, and $100$ shares of stock B with $$2$ per share and $200$ shares of stock C sold at $$0\mathrm{.}5$ per share. Let the expected returns be E$($rA$)=10\%,$ E$($rB$)=6\%$ and E$($rC$)=9\%$ respectively. The risk$-$free interest rate rf is $5\%,$ and the standard deviation for the market portfolio is sM$=20\%.$ Assume that the CAPM theory holds.

a$)$ What is the expected return E$($rM$)$ of the market portfolio? Show your work.

b$)$ What is the covariance between stock B and the market portfolio? Show your work.