Suppose we try to model the stock market the following way. Each week the market is either bullish, bearish, or stagnant. A bull week is followed by another bull week 80% of the time. A bull week is followed by a bear week 7.5% of the time. A bear week is followed by a bear week 85% of the time. A bear week is followed by a stagnant week 10% of the time. A stagnant week is followed by another stagnant week 50% of the time. Finally, a stagnant week is followed by a bull week 25%.

Set this problem up as a Markov chain. Give the states and the transition matrix.