Aremote 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, 80% will remain listening to the news after the station break that occurs each half hour, while 20% will switch to the music station at the station break. Of the listeners who are tuned to the music station, 80% will switch to the news station at the station break, while 20% will remain listening to the music. Suppose everyone is listening to the news at 8 15 AM. Complete parts a and b. a. Find the steady-state vector for the Markov chain. Find the steady-state vector for the Markov chain. Choose the correct answer below. (Type integers or decimals) O A. 9= O B. 9 Oc. q= b. At some point late in the day, what fraction of the listeners will be listening to the news? Late in the day % of the listeners will be listening to the news. (Round to the nearest percent as needed.)

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A 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, 80% will remain listening to the news after the station break that occurs each half hour, while 20% will switch to the music
station at the station break. Of the listeners who are tuned to the music station, 80% will switch to the news station at the station break, while 20% will remain listening to the music. Suppose everyone is listening to the news at 8:15 A.M. Complete parts a and b.
a.
Find the steady-state vector for the Markov chain.
Find the steady-state vector for the Markov chain. Choose the correct answer below.
(Type integers or decimals.)
O A. q=
O B. q=|
Oc. q=
b. At some point late in the day, what fraction of the listeners will be listening to the news?
Late in the day % of the listeners will be listening to the news.
(Round to the nearest percent as needed.)
OI O DI
Transcribed Image Text:A 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, 80% will remain listening to the news after the station break that occurs each half hour, while 20% will switch to the music station at the station break. Of the listeners who are tuned to the music station, 80% will switch to the news station at the station break, while 20% will remain listening to the music. Suppose everyone is listening to the news at 8:15 A.M. Complete parts a and b. a. Find the steady-state vector for the Markov chain. Find the steady-state vector for the Markov chain. Choose the correct answer below. (Type integers or decimals.) O A. q= O B. q=| Oc. q= b. At some point late in the day, what fraction of the listeners will be listening to the news? Late in the day % of the listeners will be listening to the news. (Round to the nearest percent as needed.) OI O DI
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