Let the probability density function of X and Y be bivariate normal. For what values of a is the variance of aX+Y minimum?
The answer in the book is -p(X,Y)(std dev of X/std dev of Y)
The Attempt at a Solution
I think the equation for Var(aX+Y) is,
Var(aX+Y)=a^2Var(X)+Var(Y)+2aCov(X,Y), but I have no idea how to work this equation to equal the answer in the book.
Any ideas would be much appreciated!!