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suppose that there are two bins containing 2m balls total always with m balls in

ID: 2979280 • Letter: S

Question

suppose that there are two bins containing 2m balls total always with m balls in each of the two bins. there are a white balls and b black balls.(a+b=2m) at each unit time from each bin a ball is selected, and the two balls are exchanged. let X be the number of white balls in the first bin, after t steps. (a)find the transition probabilities for X. (b)find the stationary distribution. (c)If m=3=a ,at the chain starts with a single white ball in the first bin, what is the expected time until all the white balls are in the first bin?

Explanation / Answer

suppose that there are two bins containing 2m balls total always with m balls in each of the two bins. there are a white balls and b black balls.(a+b=2m) at each unit time from each bin a ball is selected, and the two balls are exchanged. let X be the number of white balls in the first bin, after t steps. (a)find the transition probabilities for X. (b)find the stationary distribution. (c)If m=3=a ,at the chain starts with a single white ball in the first bin, what is the expected time until all the white balls are in the first bin?