Given a parameter 0 p 1, consider the Markov chain with state space = {1, 2, 3, 4, 5} and transition matrix

(i) Depending on the parameter p, identify the transient states and the classes of recurrent states. Also determine the period of each state.

(ii) Depending on p, for each recurrent class, find the stationary distribution for the chain restricted to that class. Determine all stationary distributions for the full chain.