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Bernoulli–Laplace model of diffusion. Consider two urns each of which contains m balls; b of…


Bernoulli–Laplace model of diffusion. Consider two urns each of which contains m balls; b of these 2m balls are black, and the remaining 2m – b are white. We say that the system is in state i if the first urn contains i black balls and m – i white balls while the second contains b i black balls and m – b + i white balls. Each trial consists of choosing a ball at random from each urn and exchanging the two. Let Xn be the state of the system after n exchanges have been made. Xn is a Markov chain. (a) Compute its transition probability. (b) Verify that the stationary distribution is given by.

Bernoulli–Laplace model of diffusion. Consider two urns each of which contains m balls; b of...

(c) Can you give a simple intuitive explanation why the formula in (b) gives the right answer?