Let [math]X[/math] and [math]Y[/math] be independent random variables with uniform densities in [math][0,1][/math]. Let [math]Z = X + Y[/math] and [math]W = X - Y[/math]. Find

• [math]\rho(X,Y)[/math] (see Exercise).
• [math]\rho(X,Z)[/math].
• [math]\rho(Y,W)[/math].
• [math]\rho(Z,W)[/math].