
Markov Chain Problem
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.

I have tried and tried to work this out. I feel like crying.
I know its a birth death process, and based on Ehrenfest's diffusion model, but I have been trying to work this problem out for a week now and have not solved anything. Can anyone please help (Crying)