2. A rat runs through the maze shown below. At each step it leaves the room it is in by choosing at random one of the doors out of the room. 2 1 3 4 + 5 6 (a) Write down the transition matrix for this Markov chain. [2] (b) What are the communicating classes for this Markov chain? Are they periodic? Justify your answer. [2] (c) Find the stationary distribution for this Markov chain. Demonstrate that it is the stationary distribution (i.e. do not simply write down a 7 with no justification) [3]