Suppose that X,Y∼Unif(0,1)X,Y \sim \text{Unif}(0,1)X,Y∼Unif(0,1) IID. Define U=1−X2−Y2U = 1 - X^2 - Y^2U=1−X2−Y2 and V=X2+Y2V = X^2 + Y^2V=X2+Y2. Find Cov(U,V)(U,V)(U,V).
