How do I solve for this problem?

I appreciate good handwriting and typing. I will rate your answer as "helpful". Thanks!

3. You have $1 to invest in two assets. We denote by R), i = 1,2, the yearly return from asset i. This means that every dollar invested in asset i will turn into $(1 + R1). Denote by a 6 [0,1] the amount you invested in asset 1. Then the return of your portfolio is R = aR1 + (1 a)R2. Suppose that R1 and R2 are continuous random variables With E(R1) = E(R2) = 0.1, Var(R1) = 0.04 and Var(R2) = 0.09. (a) Suppose that R1 and R2 are independent. i. Find the value of a which minimizes the standard deviation (and / or variance) of the portfolio return R. ii. For the value of a that you obtain in i), nd E(R) and var(R). (b) Suppose now that R1 and R2 are correlated, With covariance COV(R1, R2) = 0.03. i. Compute Corr(R1, R2). ii. Find the value of a which minimizes the standard deviation (and / or variance) of the portfolio return R. iii. For the value of a that you obtain in ii), nd E(R) and var(R)