The special properties of HMMs make them very simple to use. Later, this will help us create elegant algorithms for doing computations with HMMs.
Conditional independence of observations
The HMM assumes each observation is independent of all the others, given the state that emitted it.
What is "hidden" ?
The model can use many possible state sequences to generate any given observation sequence. We don't know which one it used, and we don't care!
