Science:Math Exam Resources/Courses/MATH152/April 2016/Question B 04 (a)/Hint 1

The set of states $\{s_{1},s_{2},\cdots ,s_{n}\}$ is given and each state can move to the other states or stay the same state on each step.

Then, we define transition probability $p_{ij}$ by the probability that the current state $s_{j}$ move to the state $s_{i}$ in the next step.

In the question, we have two states $s_{1}=$city and $s_{2}=$suburb and 1 year corresponds to one step. Then, the transition probability $p_{21}$, for example, means that $p_{21}$ percent of city residents move to the suburbs in one year.