I need an explanation!

Question:

a) In this section, state vectors are probability vectors. What does x, represent in 4.9 Example 1? b) Markov Chains are defined recursively: X] =PX , for k =0,1,2,... Write a Markov Chain for Example 1: c) Your Markov Chain from part (b) is just a matrix-vector form of two migration equations. Let Ck and s, represent the city and suburban percentages. Write the two migration equations. CK+1 = d) Show how to compute x, for Example 1.EXAMP LE 1 Section 1.10 examined a model for population movement between a city and its suburbs. See Figure l. The annual migration between these two parts of the metropolitan region was governed by the migration matrix M : From: City Suburbs To: 10 .95 .03 City '115 .9? Suburbs That is, each year 5% of the city population moves to the suburbs, and 3% of the suburban population moves to the city. The columns of M are probability vectors, so M is a stochastic matrix. Suppose the 2014 population of the region is 600,000 in the city and 400,000 in the suburbs. Then the initial distribution of the population in the region is given by x.) in (1) above. What is the distribution of me population in 2015'? In 2016? FIBURE 1 Annual percentage migration between city and suburbs