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Q4 (a) (b) After studying a brand-switching problem, an analyst concluded that Brand A loses 20 percent of its customers each period to Brand B and 10 percent to Brand C. Brand B loses 10 percent of its customers each period to Brand A and 30 percent to Brand C. Brand C loses 30 percent to Brand A and 20 percent to Brand B. Tabulate the matrix of transition probabilities. A rural community has two television stations, and each Wednesday night the local viewers watch either the Wednesday Movie or a show called Western Times. Table Q4 shows the transition matrix which contains the probabilities of a viewer's watching one of the shows in a week, given that he or she watched a particular show the preceding week. (ii) This week Wednesday Movie Western Times (iii) Table Q4: Transition matrix Compute the steady-state probabilities. Next week Wednesday Movie 0.75 0.45 Western Times 0.25 0.55 Compute the number of television sets tuned to each show in the long run assuming that the community contains 1,200 television sets. A prospective local sponsor wanted to pay for commercial time on one of the shows. Determine which show would more likely be selected.

Q4 (a) (b) After studying a brand-switching problem, an analyst concluded that Brand A loses 20 percent of its customers each period to Brand B and 10 percent to Brand C. Brand B loses 10 percent of its customers each period to Brand A and 30 percent to Brand C. Brand C loses 30 percent to Brand A and 20 percent to Brand B. Tabulate the matrix of transition probabilities. A rural community has two television stations, and each Wednesday night the local viewers watch either the Wednesday Movie or a show called Western Times. Table Q4 shows the transition matrix which contains the probabilities of a viewer's watching one of the shows in a week, given that he or she watched a particular show the preceding week. (ii) This week Wednesday Movie Western Times (iii) Table Q4: Transition matrix Compute the steady-state probabilities. Next week Wednesday Movie 0.75 0.45 Western Times 0.25 0.55 Compute the number of television sets tuned to each show in the long run assuming that the community contains 1,200 television sets. A prospective local sponsor wanted to pay for commercial time on one of the shows. Determine which show would more likely be selected.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
Problem 47E: Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.
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Q4 (b) (a) After studying a brand-switching problem, an analyst concluded that Brand A loses 20 percent of its customers each period to Brand B and 10 percent to Brand C. Brand B loses 10 percent of its customers each period to Brand A and 30 percent to Brand C. Brand C loses 30 percent to Brand A and 20 percent to Brand B. Tabulate the matrix of transition probabilities. A rural community has two television stations, and each Wednesday night the local viewers watch either the Wednesday Movie or a show called Western Times. Table Q4 shows the transition matrix which contains the probabilities of a viewer's watching one of the shows in a week, given that he or she watched a particular show the preceding week. This week Wednesday Movie Western Times Table Q4: Transition matrix Wednesday Movie 0.75 0.45 Next week Compute the steady-state probabilities. Western Times 0.25 0.55 Compute the number of television sets tuned to each show in the long run assuming that the community contains 1,200 television sets. A prospective local sponsor wanted to pay for commercial time on one of the shows. Determine which show would more likely be selected. I
Transcribed Image Text:Q4 (b) (a) After studying a brand-switching problem, an analyst concluded that Brand A loses 20 percent of its customers each period to Brand B and 10 percent to Brand C. Brand B loses 10 percent of its customers each period to Brand A and 30 percent to Brand C. Brand C loses 30 percent to Brand A and 20 percent to Brand B. Tabulate the matrix of transition probabilities. A rural community has two television stations, and each Wednesday night the local viewers watch either the Wednesday Movie or a show called Western Times. Table Q4 shows the transition matrix which contains the probabilities of a viewer's watching one of the shows in a week, given that he or she watched a particular show the preceding week. This week Wednesday Movie Western Times Table Q4: Transition matrix Wednesday Movie 0.75 0.45 Next week Compute the steady-state probabilities. Western Times 0.25 0.55 Compute the number of television sets tuned to each show in the long run assuming that the community contains 1,200 television sets. A prospective local sponsor wanted to pay for commercial time on one of the shows. Determine which show would more likely be selected. I
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