Hidden Markov Models (HMM)
In an HMM, you don’t know the state sequence that the model passes through, but only some probabilistic function of it.
Example: The crazy soft drink machine: it can be in two states, cola preferring and iced tea preferring, but it switches between them randomly after each purchase according to some probabilities.
The question is: What is the probability of seeing the output sequence {lemonade, iced-tea} if the machine always starts off in the cola preferring mode.