2- Every year- people move between urban (U)- suburban (S)- and rural.docx

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This document discusses the movement of people between urban, suburban, and rural populations each year based on given probabilities. It asks to construct a stochastic matrix describing the movement and explain what the Perron-Frobenius theorem tells us about the existence of a steady-state vector and behavior of the Markov chain.

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2. Every year, people move between urban (U), suburban ( S ) , and rural ( R ) populations with
the probabilities given in Figure 4.5.12. Figure 4.5.12. The flow between urban, suburban, and
rural populations. a. Construct the stochastic matrix A describing the movement of people. b.
Explain what the Perron-Frobenius theorem tells us about the existence of a steady-state vector q
and the behavior of a Markov chain.

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