Consider two dogs (Spot and Lassie) suffering from a total number of $\displaystyle m$ fleas. Spot initially has $\displaystyle b$ fleas and Lassie initially has the remaining $\displaystyle m - b.$ The fleas have

agreed on the following immigration policy: at times $\displaystyle n = 1,2.... $ a flea is selected uniformly at random from the total population and that

flea will jump from one dog to the other.

Describe the flea population on Spot as a Markov chain and find the stationary distribution $\displaystyle \pi$ of the chain.