Consider an E = {0, 1, 2, 3, 4}-valued Markov chain {Xn; n ∈ N} with transition matrix
where 0
1. Show that the chain {Xn} is irreducible and recurrent. Denote its invariant probability by π.
2. Show that under P0, the law of T is a geometric law to be specified. Show that E0(T ) = (p + 1)/p.Q