Chapter 4.9, Problem 11E

1. a. Find the steady-state vector for the Markov chain in Exercise 1.
2. b. At some time late in the day, what fraction of the listeners will be listening to the news?

1. A small remote village receives radio broadcasts from two radio stations, a news station and a music station. Of the listeners who are tuned to the news station, 70% will remain listening to the news after the station break that occurs each half hour, while 30% will switch to the music station at the station break. Of the listeners who are tuned to the music station, 60% will switch to the news station at the station break, while 40% will remain listening to the music. Suppose everyone is listening to the news at 8:15 A.M.

1. a. Give the stochastic matrix that describes how the radio listeners tend to change stations at each station break. Label the rows and columns.
2. b. Give the initial state vector.
3. c. What percentage of the listeners will be listening to the music station at 9:25 A.M. (after the station breaks at 8:30 and 9:00 A.M.)?