A major long-distance telephone company (company A) has studied the tendency of telephone users to switch from one carrier to another. The company believes that over successive six-month periods, the probability that a customer who uses A's service will switch to a competing service is 0.2 and the probability that a customer of any competing service will switch to A is 0.3. (a) Find a transition matrix for this situation. (b) If A presently controls 60% of the market, what percentage can it expect to control six months from now? (c) What percentage of the market can A expect to control in the long run? (a) Find a transition matrix for this situation. Let "Comp" stand for "a competing service." A Comp A Comp (Type integers or decimals.) (b) If A presently controls 60% of the market, what percentage can it expect to control six months from now? Company A can expect to control% of the market six months from now. (c) What percentage of the market can A expect to control in the long run? Company A can expect to control% of the market in the long run.

A major long-distance telephone company (company A) has studied the tendency of telephone users to switch from one carrier to another. The company believes that over successive six-month periods, the probability that a customer who uses A's service will switch to a competing service is 0.2 and the probability that a customer of any competing service will switch to A is 0.3. (a) Find a transition matrix for this situation. (b) If A presently controls 60% of the market, what percentage can it expect to control six months from now? (c) What percentage of the market can A expect to control in the long run? (a) Find a transition matrix for this situation. Let "Comp" stand for "a competing service." A Comp A Comp (Type integers or decimals.) (b) If A presently controls 60% of the market, what percentage can it expect to control six months from now? Company A can expect to control% of the market six months from now. (c) What percentage of the market can A expect to control in the long run? Company A can expect to control% of the market in the long run.

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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