Hi, I am looking for assistance on the following stochastic processes problem - Markov chains

1.9 Consider the Markov chain w:thstatespaee{1,2, .311\" 5 _1 2 n - : :1 0-1/3 2/3 0 0' 52150 0 0 1/43/4 " P: 3 0 0 0 1/21/2 4 1 0 0 0 0 5 1 O 0.00 (a) Is the chain irreducible? (b) What is the period of the chain? (C) What are P1,ooo(2a'1),P1,ooo(2,2),P1,000(2,4) (approximately)? _ (d) Let T be the rst return time to the state 1, starting at state 1. What is the distribution of T and what is E (T)? What does this say, without any further calculation, about 1r(l)? (e) Find the invariant probability fr; Use this to nd the expected return time to state 2, starting in state 2