Ehrenfest Chain. Consider a system in which ν particles move in discrete time between two locations 1 and 2. At each time period, a particle chosen at random moves from its location to the other one....

Ehrenfest Chain. Consider a system in which ν particles move in discrete time between two locations 1 and 2. At each time period, a particle chosen at random moves from its location to the other one. Let
_Xn
denote the number of particles in location 1 at time n. Justify that
_Xn
is an irreducible Markov chain with period 2 and show that its stationary distribution is a binomial distribution.