Let X (t) be a birth and death process with possible states 0, 1, ..., N and birth rate ?i = ?(N ? i)and Solution Let the size of the finite state space E = k, Then the stationary probabilities are Prob(X = a) = 1/k for any a in E. Because P is doubly stochastic it is very easy to check that indeed the vector (1/k,....,1/k) is stationary w.r. to P..