Simple question on variance

Quote:

Originally Posted by Dream

Let X and Y be random variables with mean E(x)= u(1) = 1, E(y)=u(2) = 4, and variance, var(x) = 4, var(y) = 6 , and roe, p = 1/2.
Find the mean and the variance of Z = 3x -2y. The answers are -5 and 30.6

How did they get this? I know that
var(z) = var(3x) + var(-2y) +2Cov(xy)

I am not getting the right answer out for variance, and I don't really have any idea on finding the mean. Can someone break it down to me? Thanks.

Things you're expected to know and use: If $Z = aX + bY$ then:

$E(Z) = a E(X) + b E(Y)$

$Var(Z) = a^2 Var(X) + b^2 Var(Y) + 2ab Cov(X, Y)$

$\rho = \frac{Cov(X, Y)}{\sigma_X \sigma_Y} \Rightarrow Cov(X, Y) = \rho \, \sigma_X \, \sigma_Y$