Data collected from selected major metropolitan areas in the eastern United States show that 2% of individuals living within the city limits move to the suburbs during a one-year period while 1% of individuals living in the suburbs move to the city during a one-year period. Answer the following questions, assuming that this process is modeled by a Markov process with two states: city and suburbs: a. prepare the matrix of transition probabilities.

b. Compute the steady-state probabilities.

c. In a particular metropolitan area, 40% of the population lives in the city, and 60% of the population lives in the suburbs. What population changes do your steady-state probabilities project for this metropolitan area?