36. Diffusion, osmosis. Markov chains are defined by the following procedures at any time n: (a) Bernoulli model. Two adjacent containers A and B each contain m particles; m are of type I and m are of type II. A particle is selected at random in each container. If they are of opposite types they are exchanged with probability a if the type I is in A, or with probability ß if the type I is in B. Let Xn be the number of type I particles in A at time n. (b) Ehrenfest dog-flea model. Two adjacent containers contain m particles in all. A particle is selected at random. If it is in A it is moved to B with probability a, if it is in B it is moved to A with probability B. Let Yn be the number of particles in A at time n. In each case find the transition matrix and stationary distribution of the chain.

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