Five balls are distributed between urn A and urn B. At each step, an urn is selected at random and ball from that urn is moved to the other urn, if the selected urn isn't empty. If the chosen urn is empty, no ball is moved. The state of the system is the number of balls in urn A.
(a) Determine the transition matrix of this Markov Chain.
(b) Determine its stationary distribution.
(c) If urn A is now empty, how long must we wait on average until it is empty for the next time?