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A small remote village receives radio broadcasts from two
Chapter 4, Problem 1E(choose chapter or problem)
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.
a. Give the stochastic matrix that describes how the radio listeners tend to change stations at each station break. Label the rows and columns.
b. Give the initial state vector.
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.)?
Questions & Answers
QUESTION:
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.
a. Give the stochastic matrix that describes how the radio listeners tend to change stations at each station break. Label the rows and columns.
b. Give the initial state vector.
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.)?
ANSWER:Solution 1E
(a)
Of the listeners who are tuned the News station, 70% listeners are stay tuned to the News station after station break after each half hour while 30% are switch to music station.
Of the listeners who are tuned the Music station, 40% listeners are stay tuned to the music station after station break after each half hour while 60% are switch to News station.
Construct the stochastic matrix as below,
From/To |