You invest $$300,000$ in Stock X$,$ $$200,000$ in Stock Y$,$ and $$500,000$ in Stock Z$.$

a$)$ The betas for Stocks X$,$ Y$,$ and Z are $0\mathrm{.}90,1\mathrm{.}25,$ and $1\mathrm{.}80,$ respectively. Find the beta of the portfolio.

b$)$ The risk free rate of return is $5$ percent and the return on the market portfolio is $11$ percent. Find the expected return on the portfolio according to the Capital Asset Pricing Model $($CAPM$)?$