Let $(X,Y,Z,N_X,N_Y,N_Z)$ be a discrete random vector such that $N_X,N_Y,N_Z$ has an expected value of $0$, variance of $1$, are mutually independent and $$X=N_x$$ $$Y=-X+N_Y$$ $$Z=X+2Y+N_Z$$
Calculate $E(X)$, $E(Y)$, $E(Z)$, $var(X)$, $var(Y)$, and $Var(Z)$.
So far I've substituted $X$ with $N_X$ and $Y$ with $N_Y-N_x$. But I'm not sure what to do after this. This gives me the following: $$X=N_X$$ $$Y=N_Y-N_X$$ $$Z=2N_Y+N_Z-N_X$$
$EX=EN_X=0$, $EY=-EX+EN_Y=0,EZ=EX+2EY+EN_Z=0$ and $$var (X) =var (N_X)=1,$$ $$ var (Y)=var (-X+N_Y)$$ $$= var (-N_X+N_Y)=var (-N_X)+var (N_Y)=2,$$ $$ var (Z)=var (-N_X+2N_Y+N_Z)=1+4+1=6.$$