Suppose the city of Metropolis is experiencing a movement of its population to the suburbs. Each...

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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. 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.