Find the Steady-State Probability Vector for the Stochastic Matrix P. -Suppose That Demographic Studies Show That Each Year About 8

Find the steady-state probability vector for the stochastic matrix P.
-Suppose that demographic studies show that each year about 8% of a cityʹs population moves to the suburbs (and 92% stays in the city) , while 4% of the suburban population moves to the city
(and 96% remains in the suburbs) . In the year 2000, 64.1% of the population of the region lived in
The city and 35.9% lived in the suburbs. What percentage of the population of the region would
Eventually live in the city if the migration probabilities were to remain constant over many years?
For simplicity, ignore other influences on the population such as births, deaths, and migration into
And out of the region.

A) 66.7%
B) 50%
C) 41.7%
D) 33.3%