Create a hidden Markov model to predict the half inning score sequence of an American baseball game. Suppose the half inning sequence is 0, 0, 0, 1, 0, 1, 1, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0. For simplicity, constrain the scoring for each team to 0, 1, or 2 runs during their half inning at bat.

a. How would you change the model to allow any number of runs per half inning?

b. How might you train your system to obtain more realistic score values?