Suppose the city of Metropolis is experiencing a movement of its population to the suburbs. Each year suburbs, while only 5% of the people that live in the suburbs move into the city. The rest stay where they are. a. Write a transition matrix to represent the population movement. b. Currently 70% of the population lives in the city of Metropolis and 30% lives in the suburbs. What percentage of the population will live in the city after two years? c Find the steady-state probability vector X = of the Markov chain to give the long term distribution of the population of Metropolis.

Suppose the city of Metropolis is experiencing a movement of its population to the suburbs. Each year suburbs, while only 5% of the people that live in the suburbs move into the city. The rest stay where they are. a. Write a transition matrix to represent the population movement. b. Currently 70% of the population lives in the city of Metropolis and 30% lives in the suburbs. What percentage of the population will live in the city after two years? c Find the steady-state probability vector X = of the Markov chain to give the long term distribution of the population of Metropolis.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Suppose the city of Metropolis is experiencing a movement of its population to the suburbs. Each year 25% of the people that live in the city move to the
suburbs, while only 5% of the people that live in the suburbs move into the city. The rest stay where they are.
a. Write a transition matrix to represent the population movement.
b. Currently 70% of the population lives in the city of Metropolis and 30% lives in the suburbs. What percentage of the population will live in the city
after two years?
c. Find the steady-state probability vector X =
of the Markov chain to give the long term distribution of the population of Metropolis.

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