a)Does any one know what to do to the variance when multiplied by a number? I know that when added together:

$Z = X + Y => Var(Z) = Var(X + Y)$

I seem to remember something like:

$Z = aX => Var(Z) = a^2Var(X)$

This may be completely wrong... Any ideas?

b)Since the equation for the correlation coefficient is

$p(x,y) = \frac{cov(X,Y)}{\sqrt{var(X)}\sqrt{var(Y)}}$