Consider a Markov Chain with state space S = {1,2,..., 14, 15} and transition probability matrix P1 P2 P3 P4 P15 P1 P2 P3 P14 P15 P1 P2 P = P15 P14 P13 ⠀⠀⠀⠀⠀⠀ P2 P3 P4 P5 P1 where 0 < P1, P2 < 1, p₁ + P2 + ... + P15 = 1. Find limn→∞ Pn.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Consider a Markov Chain with state space S
=
{1,2,..., 14, 15} and transition probability matrix
P1 P2 P3 P4
P15 P1 P2 P3
P14 P15 P1 P2
P =
P15
P14
P13
⠀⠀⠀⠀⠀⠀
P2 P3 P4 P5 P1
where 0 < P1, P2 < 1, p₁ + P2 + ... + P15 = 1. Find limn→∞ Pn.
Transcribed Image Text:Consider a Markov Chain with state space S = {1,2,..., 14, 15} and transition probability matrix P1 P2 P3 P4 P15 P1 P2 P3 P14 P15 P1 P2 P = P15 P14 P13 ⠀⠀⠀⠀⠀⠀ P2 P3 P4 P5 P1 where 0 < P1, P2 < 1, p₁ + P2 + ... + P15 = 1. Find limn→∞ Pn.
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