4) (20 points) A Markov Chain model for a rat wandering through the following maze. At the end of each period, the rat is equally likely to leave its current room through any of the doorways. (It never stays in the same room.) Room 1 and 5 are absorbing states. 1 t.tt a) (4 pts.) Write out the transition matrix for this Markov chain with the absorbing states listed first. b) (7pts.) Compute the fundamental matrix N. c) (5 pts.) What is the expected number of rounds until absorption if the rat starts in room 2? d) (4 pts.) What is the probability of the rat ending up in room 1 if the rat starts in room 2