a) Let $X$ and $Y$ be two uncorrelated random variables. Assume $Var(X) = 1.55$ and $Var(Y) = 0.8$. What is the variance of the random variable $Z = -4X + 5Y - 6$?
b) What if $X$ and $Y$ are correlated with $Cov(X,Y) = 0.6$?
For a) since the variables are uncorrelated I thought you could just sum the variances of the variables? So $$Var(Z) = -4Var(X) + 5Var(Y)$$ However this produces an incorrect answer.