Show that the Markov chain of Example 7.12 is irreducible and aperiodic if0 < qi < 1 for

Chapter 7, Problem 4

(choose chapter or problem)

Show that the Markov chain of Example 7.12 is irreducible and aperiodic if0 < qi < 1 for all i. Also show that if for some j, 1 j m, qj = 0, then thechain is not irreducible. Finally show that if qj = 1 for some j, 1 j m, thenthe chain is periodic.

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