Let f (x1, x2) be a joint p.d.f. Suppose that (X(i)1 , X(i)2) has the joint p.d.f. f . Let (X(i+1)1, X(i+1)2) be the result of applying steps 2 and 3 of the Gibbs sampling algorithm on page 824. Prove that (X(i+1)1, X(i)2) and (X(i+1)1 , X(i+1)2) also have the joint p.d.f. f .