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transition matrix A B C A 0.7 0.2 0.1 B 0.1 0.6 0.3 с 0.2 0.2 0.6 a) Find the long-term market share for each brewery.

transition matrix A B C A 0.7 0.2 0.1 B 0.1 0.6 0.3 с 0.2 0.2 0.6 a) Find the long-term market share for each brewery.

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• 1. Brewery A is analyzing its market position against its two competitors, brewery B and brewery C. A customer switches among corresponding brands of vodka (A, B, and C) according to a Markov chain with the following one-step transition matrix A B C A 0.7 0.2 0.1 B 0.1 0.6 0.3 C 0.2 0.2 0.6 a) Find the long-term market share for each brewery. b) Find the probability of the following sequence of preference switching: from A to B to C to A. c) Find the probability of the following sequence of preference switching: from A to C to B to A.
Transcribed Image Text:• 1. Brewery A is analyzing its market position against its two competitors, brewery B and brewery C. A customer switches among corresponding brands of vodka (A, B, and C) according to a Markov chain with the following one-step transition matrix A B C A 0.7 0.2 0.1 B 0.1 0.6 0.3 C 0.2 0.2 0.6 a) Find the long-term market share for each brewery. b) Find the probability of the following sequence of preference switching: from A to B to C to A. c) Find the probability of the following sequence of preference switching: from A to C to B to A.
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