Question

1. (20 points total) A small town receives radio broadcast from two radio stations, a news station (N) and a music station (M). Of the listeners who are tuned to the news station, 75% will remain listening to news after the station break that occurs each half hour, while the other listeners wll switch to the music station at the station break. Of the listeners who are tuned to the music station, 40% will switch to the news station at the station break, while the other listeners will stay tuned to the music station after the break. Suppose everyone is listening to the news station at 7:10am (a) (4 points) What is the stochastic matrix P (also called transition or probability matrix) that describes how the radio listeners tend to change stations at each station break. Label the rows and columns so that N proceeds M b) (1 point) What the initial state vector xo? (c) (5 points) What percentage (approximately) of the listeners will be listening to the music station at 8:40am (after the station breaks at 7:30am, 8:00am, and 8:30am)? Use a calculator or CAS but leave your answers in fractional form until you compute the percentages d) (10 points) Find the steady-state vector of the stochastic matrix P from part (a)

Answer 1

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, 025 0-25 1-16y: o Sub y in O 5 2 6 13 0.61 53 | 3 0.3846 6-3846 Sleady- stale vecdoys O.6153 News S Scanned with CamScanner