How to find the combined expected value

Question

Say we have expected values:

$E(X) = E(Y) = 0.4$

And variance:

$V(X) = 2$ and $V(Y) = 1$

and the correlation between X and Y is $\rho(X,Y) = 0.3$

How do I find the expected value and variance for

$U = X + Y$ and $W = 2Y$

And the correlation between $U$ and $W$?

I have tried to solved it this way it, but I think its wrong:

$E(X+Y) = 0.4 + 0.4 = 0.8$

Answer 1

Hint: $$ \text{Cov}(U,W)=\text{Cov}(X+Y,2Y) = 4( \text{Cov}(X,Y) + \text{Var}(Y)) $$