Two movie theatres that show several different movies each night compete for the

Question

Two movie theatres that show several different movies each night compete for the same audience. Of the people who attend Theatre A one night, 10% will attend again the next night and 5% will attend Theatre B the next night. Of the people who attend Theatre one night, 8% will attend again the next night and 6% will attend Theatre A the next night. Of the people who attend neither theatre one night, 3% will attend Theatre A the next night and 4% will attend Theatre B the next night. Find and interpret the state matrix for this situation.

Explanation / Answer

Ans:

There will be three states for this Discrete time markov chain:Theater A,Theater B,neither

Transition probability matrix,P:

(Each row of the transition probability matrix should sum up 1)

Theater A Theater B neither Theater A 0.1 0.05 0.85 Theater B 0.06 0.08 0.86 neither 0.03 0.04 0.93

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