$1.$ For problems $1$ and $2,$ use the following data: risk$-$free rate is $1\mathrm{.}5\%$; expected return of the market portfolio M is $9\mathrm{.}69\%$; standard deviation of the market return is $20\%.$Your roommate wants advice on how to invest her $$55,000$ inheritance. She wants to keep $$15,000$ in safe investments but is willing to risk the other $$40,000.$ According to the CML$,$ what are her expected return and standard deviation? $2.$ You have $$100,000$ to invest.a$)$ What are the mean return and standard deviation of your portfolio, if you invest $$50,000$ in a risk$-$free asset and $$50,000$ in the market portfolio M$?$b$)$ You decide that the $50/50$ portfolio is too tame and decide to take on more risk. You invest $$95,000$ in the market portfolio M and only $5\%$ in the risk$-$free asset. What are the expected return and standard deviation?