Given two uncorrelated random variables $X,Y$ with the same variance $\sigma^2 $ I need to compute $\rho= \frac{COV(X,Y)}{\sigma(X)\sigma(Y)}$ between $X+Y$ and $2X+2Y$. I know it should be a number between $-1$ and $1$ and I don't understand how come I get $4$.
Here's what I did:
$COV(X+Y,2X+2Y)=COV(X+Y,2X)+COV(X+Y,2Y)=COV(2X,X)+COV(2X,Y)+COV(2Y,Y)+COV(2Y,X)=2COV(X,X)+2COV(Y,Y)+4COV(X,Y)=2\sigma^2+2\sigma^2=4\sigma^2$ so final result is $\rho=4$ since $\sigma(X)=\sqrt{Var(x)}$.
What's wrong with what I did?