Exercise 5

A certain town is in a certain country (this is a hypothetical problem). Each year ten percent of the town dwellers move to other parts of the country. Each year one percent of the people from elsewhere move to the town. Assume that there are two states $s_{T}$, living in town, and $s_{C}$, living elsewhere.

• Construct the transition matrix.

• Starting with an initial distribution $s_{T}=0.3$ and $s_{C}=0.7$, get the results for the first ten years.

• Do the same for $s_{T}=0.2$.

• Are the two outcomes alike or different?