1.       Predict the probabilities of categories Cat and Car of Test2 on the toy corpus example in Sect. 5.3.5.2. You can use the multinomial na¨ıve Bayes model with the same level of smoothing as used in the example in the book. Return normalized probabilities that sum to 1 over the two categories.

2.       Na¨ıve Bayes is a generative model in which each class corresponds to one mixture component. Design a fully supervised generalization of the nai¨ıve Bayes model in which each of the k classes contains exactly b > 1 mixture components for a total of b · k mixture components. How would you perform parameter estimation in this model?