Let $U=2X$ and $V=-3Y$. Find Correlation (U,V) given Correlation $(X,Y)=0.8$.
My Steps:
$$\begin{align} Correlation (U,V) & = \dfrac{Cov(U,V)}{\sqrt{Var(U)\cdot Var(V)}} \\ & = \dfrac{Cov(2X,-3Y)}{\sqrt{Var(2X)\cdot Var(-3Y)}} \\ & = \dfrac{(-6)Cov(X,Y)}{\sqrt{4Var(X)\cdot 9Var(Y)}} \\ & = \dfrac{(-6)Cov(X,Y)}{6\sqrt{Var(X)\cdot Var(Y)}} \\ & = \dfrac{-Cov(X,Y)}{\sqrt{Var(X)\cdot Var(Y)}} \\ & = -0.8 \\ \end{align}$$
Have I done this correctly ?