Please answer all a b c

Question 1 We consider a discrete-time Markov chain over states 0, 1, 2 in this order whose transition matrix is 1 - p 0 P P = D2 1 - p O 0 1 - p3 where O s p $ 1. Determine: (a) the values of p for which the chain is irreducible and ergodic (b) the mean proportion of long-term time that the chain passes to state 0 (c) the expected value of the time of first return to 0 from 0