Please show me the steps. Appreciate the work!

Consider a risk averse investor. He has a risk-free asset with a certain return r; = {1.05. He also considers a stock with random return rm with mean E [rm] = ll], variance 0%, = 1. The investor has mean-variance utility E [rp] hr: where I: 1.":- is a parameter, and that E[rp],o are the expected return and variance of the portfolio formed by mixing the risk-free asset and the stock. He chooses E [rp] and of, to maximize this utility. All parts below share the same setting. Part a. {It} marks) Find the optimal standard deviation of the portfolio o}, in terms of it. 4 Part b. {5 marks} liviathematicall}.r show how the the optimal standard deviation of the portfolio changes with it {increasestr decrease]