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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, 60% will remain listening to the news after the station break that occurs each half hour, while 40% 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 rounded to three decimal places as needed.) O A. 9= O B. 9=

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, 60% will remain listening to the news after the station break that occurs each half hour, while 40% 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 rounded to three decimal places as needed.) O A. 9= O B. 9=

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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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, 60% will remain listening to the news after the station break that occurs each half hour, while 40% 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 rounded to three decimal places as needed.) O A. q= O B. q= O c. 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.)
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, 60% will remain listening to the news after the station break that occurs each half hour, while 40% 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 rounded to three decimal places as needed.) O A. q= O B. q= O c. 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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