A salesman makes all sales in three cities x y and z only., Ask an Expert

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A salesman makes all sales in three cities X, Y and Z only. It is known that he visits each city on a weekly basis and never visits the same city in successive weeks. If he visits city X in a given week, then he visits city Z in next week. However, if he visits city Y or Z, he is twice as likely to visit city X than the other city. Obtain the transition probability matrix. Also determine the proportionate visits by him to each of the cities in the long run.

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