Distribution of X+Y of a bivariate normally distributed (X,Y)

Question

I need to give the distribution of $X+Y$ and $X-Y$ knowing that $(X,Y)$ is bivariate normally distributed with marginal means 1, marginal variances 1 and correlation $p=0.2$.Is it right that the marginal mean are simply $E(X)=1$ and $E(Y)=1$ ? I don't see where I should start knowing that.

Answer 1

(X,Y) is jointly normally distributed, therefore any linear combination is normally distributed, including U=X+Y, V=X-Y.

$E(U)=E(X)+E(Y)=2$ and $E(V)=E(X)-E(Y)=0$ are trivial

$var(U)=var(X)+var(Y)+2\sqrt{var(X)var(y)}p$ $var(V)=var(X)+var(Y)-2\sqrt{var(X)var(y)}p$

You can conclude easily