14.4 Consider three coins labeled 1, 2, and 3. When coin 1 is tossed, the probability that it comes up heads is 0.75 and the probability that it comes up tails is 0.25. Similarly, when coin 2 is tossed, the probability that it comes up heads is 0.25 and the probability that it comes up tails is 0.75. Finally, when coin 3 is tossed, the probability that it comes up heads is 0.5 and the probability that it comes up tails is 0.5. Assume that in an experiment that involves a sequence of tosses of these coins, the experimenter is equally likely to choose any coin during the next toss. Thus, if we denote “heads” by H and “tails” by T, the experiment can be modeled by the Markov chain as shown in Figure 14.20. Assume that the experimenter is equally likely to start a sequence of tosses with any coin.

a. What is the probability that the observation sequence {HTTHT} was emitted by the model?

b. Use the Viterbi algorithm to obtain the most likely state sequence that produced the observation sequence {HTTHT}.