See image below for question.

Suppose X and Y are random variables having nite means and variances, say, Vat-(X) = or}, Var(Y) = a; and CosLX, Y) = max, and consider the convex combinations of X and Y, namely, the random variables cX + (1 c)Y, where 0 S c g 1. (a) Find c so that VaT(CX + (1 c)Y) is minimized (13) (continued) Now assume X, Y are independent. What is the value of c that minimizes the variance of cX + {1 c)Y now? (c) {continued from [b)) Find an expression for the minimum variance of cX + (1 c)Y