A gas is placed in a container with two compartments A and B, separated by a permeable membrane such that molecules can pass trough it. The interchange is produced as follows: At regular periods a molecule is taken at random from the container (with equal probability). If the chosen molecule belongs to compartment A is passes to B and viceversa. The initial number of molecules in compartment A and B are respectively a and b. Denote by (An)nN the sequence of random variables describing the number of molecules in compartment A after n movements. a) Argue why (An)nN can be considered a stationary Markov chain and write tis state space. b) Find the matrix of transition probabilities in one and two steps. c) Determine the class of communicant states. d) Find if they exist the stationary probabilities