71. It follows from Theorem 4.2 that for a time reversible Markov chain Pij Pjk Pki = Pik Pkj Pji, for all i, j, k It turns out that if the state space is finite and Pij > 0 for all i, j, then the preceding is also a sufficient condition for time reversibility. [That is, in this case, we need only check Equation (4.26) for paths from i to i that have only two intermediate states.] Prove this. Hint: Fix and show that the equations xjPjk = πk Pkj are satisfied by j = cP/Pji, where c is chosen so that Σ,j=1.