Let X and Y be independent random variables with E(X)=E(Y)=5, var(X)=1 and var(Y)=(sigma^2)>1.
Put Z=aX + (1-a)Y, 0<=a<=1.
Find 1. the value of a that minimises var(A) and that minimum value.
2. the value of a that maximises var(Z) and that maximum value.
Help!