proof that for any two independent variables X,Y: ρ(X+Y, X−Y)=Var(X)−Var(Y)/Var(X)+Var(Y) [closed]
Solution 1:
Just use the definition
$$Cov(X+Y;X-Y)= E[(X+Y)(X-Y)]-E(X+Y)E(X-Y)$$
Expand and solve. Then use the definition of $\rho$
Just use the definition
$$Cov(X+Y;X-Y)= E[(X+Y)(X-Y)]-E(X+Y)E(X-Y)$$
Expand and solve. Then use the definition of $\rho$