A metropolitan area consisting of a city and its suburbs has a constant total population. Suppose that each year, 20% of the people in the city move to the suburbs, whereas 25% of the people in the suburbs move to the city. The transition matrix A for this situation is given. Find the resulting long-term distribution of a constant total population between the city and its suburbs. A = 0.8 0.25 0.2 0.75 The long-term distribution of the population is city, suburban. (Simplify your answers.)

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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A metropolitan area consisting of a city and its suburbs has a constant total population. Suppose that each year, 20% of
the people in the city move to the suburbs, whereas 25% of the people in the suburbs move to the city. The transition
matrix A for this situation is given. Find the resulting long-term distribution of a constant total population between the city
and its suburbs.
A =
0.8 0.25
0.2 0.75
The long-term distribution of the population is city,
(Simplify your answers.)
suburban.
Transcribed Image Text:A metropolitan area consisting of a city and its suburbs has a constant total population. Suppose that each year, 20% of the people in the city move to the suburbs, whereas 25% of the people in the suburbs move to the city. The transition matrix A for this situation is given. Find the resulting long-term distribution of a constant total population between the city and its suburbs. A = 0.8 0.25 0.2 0.75 The long-term distribution of the population is city, (Simplify your answers.) suburban.
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