Consider a Markov chain with state space S. Let d(k) denote the period of state k ∈ S. If there exist n, m > 0 such that pij(n) > 0 and pji(m) > 0, then which of the following statements is true?

Let {Xn : n ≥ 0} be a homogeneous Markov Chain on the state space S = {1, 2, 3, 4} having transition probability matrix P given by: P = 1/402/31/12 0100 1/1201/42/3 2/301/121/4 Which of the following statements about the stationary distributions of this Markov Chain is true?

Consider a Markov chain {Xn : n ≥ 1} on the state space {1, 2, 3, 4, 5} with the transition probability matrix: P = [0, 1/2, 1/2, 0, 0] [0, 0, 1, 0, 0] [0, 1/3, 0, 1/3, 1/3] [1, 0, 0, 0, 0] [0, 0, 0, 0, 1] Then, which of the following statements is true?