Chapter 9.1, Problem 59E

To determine

To graph:The transition diagram for the Markov chain that has three states, $A,B\text{ and }C$. The probability of going from state $A$ to state $B$ in one trail is $.1$, and the probability of going from the state $A$ to state $C$ in one trail is $.3$. The probability of going from state $B$ to state $A$ in one trail is $.2$, and the probability of going from state $B$ to state $C$ in one trail is $.5$. The probability of going from state $C$ to state $C$ in one trail is $.1$.

To determine

The transition matrix for the Markov chain that has three states, $A,B\text{ and }C$. The probability of going from state $A$ to state $B$ in one trail is $.1$, and the probability of going from the state $A$ to state $C$ in one trail is $.3$. The probability of going from state $B$ to state $A$ in one trail is $.2$, and the probability of going from state $B$ to state $C$ in one trail is $.5$. The probability of going from state $C$ to state $C$ in one trail is $.1$.