Consider a biased random walk with reflecting boundaries on {1, 2, 3, 4) with probability p=0.45 of moving to the left. a. Find the transition matrix for the Markov chain and show that this matrix is not regular. b. Assuming that the steady-state vector may be interpreted as occupation times for this Markov chain, in what state will this chain spend the most steps?

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Chapter1: Combinatorial Analysis
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Consider a biased random walk with reflecting boundaries on {1, 2, 3, 4) with probability p=0.45 of moving to the left.
a. Find the transition matrix for the Markov chain and show that this matrix is not regular.
b. Assuming that the steady-state vector may be interpreted as occupation times for this Markov chain, in what state will this chain
spend the most steps?
a. The transition matrix is P = -
(Type an integer or simplified fraction for each matrix element.)
Transcribed Image Text:Consider a biased random walk with reflecting boundaries on {1, 2, 3, 4) with probability p=0.45 of moving to the left. a. Find the transition matrix for the Markov chain and show that this matrix is not regular. b. Assuming that the steady-state vector may be interpreted as occupation times for this Markov chain, in what state will this chain spend the most steps? a. The transition matrix is P = - (Type an integer or simplified fraction for each matrix element.)
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