Consider a rat in a maze with four cells, indexed 1-4, and the outside (freedom), indexed by 0 (that can only be reached via cell 4). The rat starts initially in a given cell and takes a move to another cell, continuing to do so until finally reaching freedom. We assume that at each move (transition) the rat, independent of the past, is equally likely to choose from among the neighboring cells (so we are assuming that the rat does not learn from the past mistakes). This then yields a Markov chain, where Xn denotes the cell visited right after the nth move. Thus the set of possible values are (0, 1, 2, 3, 4). For example, when the rat is in cell 1, it moves next (regardless of its past) into cell 2 or 3 with probability ½. Identify the transition probability matrix for this Markov Chain?