Question

A television poll was conducted among regular viewers of the national news in a certain region where the three national networks share the same time slot for the evening news. Results of the poll indicate that 20% of the viewers watch the ABC evening news, 60% watch the CBS evening news, and 20% watch the NBC evening news. Furthermore, it was found that of those viewers who watched the ABC evening news during one week, 80% would again watch the ABC evening news during the next week, 10% would watch the CBS news, and 10% would watch the NBC news. Of those viewers who watched the CBS evening news during one week, 85% would again watch the CBS evening news during the next week, 10% would watch the ABC news, and 5% would watch the NBC news. Of those viewers who watched the NBC evening news during one week, 85% would again watch the NBC news during the next week, 10% would watch ABC, and 5% would watch CBS. (a) What share of the audience consisting of regular viewers of the national news will each network command after 2 weeks? (Round your answers to one decimal place.) ABC % CBS % NBC % (b) In the long run, what share of the audience will each network command? (Round your answers to one decimal place.)

Please show all work and explain! Thanks!

Answer 1

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AS FOR GIVEN DATA....

from aove transition matrix T=

	ABC	CBS	NBC
ABC	0.8	0.1	0.1
CBS	0.1	0.85	0.05
NBC	0.1	0.05	0.85

and initial vector Xo =[0.2 0.6 0.2]

a) after 2 weeks vectoe X2=Xo*T²

ABC= 26.8%

CBS= 49.4%

NBC= 23.8%

b)in long run

ABC=33.3 %

CBS= 33.3%

NBC= 33.3%

I HOPE YOU UNDERSTAND...

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