A total of 4 white balls and 6 black balls are distributed among two urns, urn A

Question

A total of 4 white balls and 6 black balls are distributed among two urns, urn

A and urn B, with each urn containing 5 balls. At each stage, a ball is randomly selected from

each urn and the two selected balls are interchanged (and returned to the urns). Let Xn denote

the number of black balls in urn A after the nth interchange.

(a) Find the one-step transition probability of the Markov chain Xn , n 0;

(b) Find the limiting probabilities and show that the stationary chain is time reversible. (You

may rst guess what the stationary distribution should be and then verify it.)

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A total of 4 white balls and 6 black balls are distributed among two urns, urn A

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