Create a hidden Markov model to represent the scoring sequence of an American football game where touchdowns are 6 points which can be followed by either a 0, 1, or 2 extra point attempt. Of course, there are two teams and either can score. If a team has the ball and does not score, they emit a 0. So, suppose the emit stream of scores is 6,1,6,0,3,0,6,1,0,3,0; what would your HMM look like?

a. Discuss this problem and what the best HMM might look like.

b. Test your HMM on two more made up streams of scores.

c. Track an actual game and see how well your system predicts the scoring stream.