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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 weekly basis and never visits same city in successive weeks. If he visits city X in given week, then he visits city Z in next week. Though, if he visits city Y or Z, he is twice as probable to visit city X than other city. Get transition probability matrix. Also Find out the proportionate visits by him to each of cities in the long run.

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