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Mathematics, 25.02.2020 19:55 zay179

A total of m white and m black balls are distributed among two urns, with each urn containing m balls. At each stage, a ball is randomly selected from each urn and the two selected balls are interchanged. Let Xn denote the number of black balls in urn 1 after the nth interchange.

(a) Give the transition probabilities of the Markov chain, Xn.
(b) Find the limiting probabilities; you may want to try using the detailed balance equations.

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