Let r.v.’s X and Y be independent, Z₁ = X +Y, Z₂ = X −Y. When are the r.v.’s Z₁ and Z₂ uncorrelated? Would it mean that they are independent? Let, say, (X,Y) be uniformly distributed on the square {(x,y) : |x| ≤ 1, |y| ≤ 1}. If we know X +Y, does it give an additional information about X −Y?)