Problem 2: (mean return time) Consider a Markov chain {X,} on states {0,1,2,3} with a tran- sition matrix 1 0.1 0.4 0.2 0.3 P = 0.2 0.2 0.5 0.1 0.3 0.3 0.4 1. Compute the limiting distribution (T0, T1, T2, T3) of this Markov Markov Chain%; 2. For each state i, compute (directly) m¡¡ - the average number of steps it takes to get back to i if started in i, and show that the relation m;; = 1/T; is true.
Problem 2: (mean return time) Consider a Markov chain {X,} on states {0,1,2,3} with a tran- sition matrix 1 0.1 0.4 0.2 0.3 P = 0.2 0.2 0.5 0.1 0.3 0.3 0.4 1. Compute the limiting distribution (T0, T1, T2, T3) of this Markov Markov Chain%; 2. For each state i, compute (directly) m¡¡ - the average number of steps it takes to get back to i if started in i, and show that the relation m;; = 1/T; is true.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 12EQ:
12. Robots have been programmed to traverse the maze shown in Figure 3.28 and at each junction...
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