This is an 'dishonest casino' example from Durbin, et al. 'Biological Sequence Analysis' book. A casino used two types of dice: one is a 'fair' one that has equal chance to all six numbers, and the other is a 'dishonest' one that has high chance of number 6 than the others. We have a sequence of dice numbers from the casino, and want to estimate when a dealer exchanged the dice.
We assume that the Hidden Markov Model of this example as below: