A transition probability matrix pis said to be doubly stochastic if the sum over each column equals one, i.e. sigma_i P_i, j = 1 Forall j If such a chain is irreducible and aperiodic and consists of M+1 states 0, 1, ..., M, show that the stationary distribution is given by pi_j = 1/M + 1 j = 0, 1, ..., M
