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.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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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.
Transcribed Image Text: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.
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