7. A transition probability matrix is said to be doubly stochastic if $$ P_ij = 1...

7. A transition probability matrix is said to be doubly stochastic if

$$

Σ P_ij = 1

$$

for all states j = 0, 1,..., M. If such a Markov chain is ergodic, show that

П= 1/(М + 1), j = 0, 1, ..., Μ.