17s418hw9sol.pdf - Stat 418 HW#9 Problem 9.2 3 P(T > s = e...

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Stat 418 HW #9 Problem 9.2 P ( T > s ) = e - 3 60 s Problem 9.7 By Theorem 2.1, for an ergodic Markov chain, π j = lim n →∞ P ( n ) ij exists, and the π j are the unique nonnegative solution of π j = M k =0 π k P kj (1) M j =0 π j = 1 (2) But a = 1 M +1 1 , where 1 is a row vector of 1’s, satisfies (1) and (2), i.e. a P = a . Hence 1 M +1 is thenh limiting probability, π j . Problem 9.8 P ij
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