-- 3. Let (Mo, M1, M2, ...) be a time-homogeneous discrete-time Markov chain on state space S {1,2,3} with transition matrix P and a random initial state Mo which is uniformly distributed in S. A stranger on a street claims that (Mt) is a martingale with respect to its own information. (a) Give an example of P for which the claim is true, and explain why. (2 p) (b) Give an example of P for which the claim is not true, and explain why. (2 p) (c) Write down a necessary and sufficient condition for P, under which the claim is true. (2 p)