The price of a certain stock is either 9, 10 or 11. If the price is 9 on any day, the next day's price will either be 9 or 10 with equal probability. If the price is 11, the next day's price will be either 11 or 10 with equal probability. If the price is 10, the next day's price will be either 9, 10, or 11 with equal probability.
(a) Model this as a Markov chain and write down the transition matrix.
(b) If the price is 9 on Monday, what is the probability that it will be 11 on Friday?
(c) Find the proportion of the time, in the long run, that the price will be each of the three possible values.