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## Homework Statement

Let the probability density function of X and Y be bivariate normal. For what values of a is the variance of aX+Y minimum?

## Homework Equations

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!!