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STA 4001

Stochastic Processes

Fall 2024

Homework 2

Due Oct 8-th Midnight

1. A total of m white and m black balls are distributed among two urns, with each urn containing m balls. Ateach 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, n ≤ 0.

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