The door outside the Dean's ofce has a sign that can be in one of three positions A= Available B=Busy C=In Class They plan to update this every hour. Every time she goes to class. she remembers with probability 0.9 to set the sign to 0 Every time she is busy, she remembers to set the sign to B with probability {1.6. Every time she is available. she remembers to set the sign to A with probability {1.3. If she forgets. the sign stays where it was the previous period. Assume that every hour. the Dean is equally likely to be doing any one of the titres activities. a) Find the transition matrix. b) Does it satisfy the conditions to be considered a MC? c) The door currently says E. Find the probability it will say A in two hours. d) You cant really see the sign, but you think its equally likely to be a or E. Find the probability that it will not say C in two hours