Chapter 10.1, Problem 34E

(a)

To determine

To verify: The transition matrix for the provided information is

$\left[\begin{array}{ccc}\frac{1}{2}& \frac{1}{3}& \frac{1}{6}\\ \frac{1}{2}& \frac{1}{3}& \frac{1}{6}\\ 0& \frac{1}{2}& \frac{1}{2}\end{array}\right]$.

(b)

To determine

The transition matrix for a two-minute period.

(c)

To determine

The probability that the number of people in the queue would change from 0 to 2 in two minutes.