1. Compute P(X=00111) for the example HMM from the slides.

2. Perform Viterbi search for X=01011 for the example HMM from the slides.

3. The typical phone HMM has emission distributions of the form P(Xi|Si, Si-1). This is different from the form that we have been using where the emission probability only depends on Si: P(Xi|Si). Show how to convert an HMM with emissions on the edges to have emissions on the nodes (states) instead. Describe the states, transition probability distributions, and emission distributions of the transformed HMM.