3.5. You are going to successively flip a quarter until the pattern HHT appears; that is, until you observe two successive heads followed by a tails. In order to calculate some properties of this game, you set up a Markov chain with the following states: 0, H, HH, and HHT, where 0 represents the starting point, H represents a single observed head on the last flip, HH represents two successive heads on the last two flips, and HHT is the sequence that you are looking for. Observe that if you have just tossed a tails, followed by a heads, a next toss of a tails effectively starts you over again in your quest for the HHT sequence. Set up the transition probability matrix.