Let {X0, X1, ...} be an irreducible Markov chain with state space and with the doubly stochastic transition matrix P = ((pij)), i.e. (1) Prove that the stationary distribution of {X0, X1, ...} is...

Let {X₀, X₁, ...} be an irreducible Markov chain with state space

and with the doubly stochastic transition matrix P = ((p_ij)), i.e.

(1) Prove that the stationary distribution of {X₀, X₁, ...} is given by

(2) Can {X₀, X₁, ...} be a transient Markov chain?