Assignment 3

1. Make up an interesting (or entertaining) example showing that Pr(x|y) can be very different from Pr(y|x). (Should take 5 minutes)

2. Use the definition of conditional probability to derive Bayes's Theorem. It may be a while since you used your high-school algebra, but that's all this requires. (If you have not completed this in 10 minutes, don't bother doing it, just look at the solution when I give it out.)

3. Do Exercise 6.1 in Jurafsky and Martin. That is, show the formula for the maximum likelihood estimate of probability in a trigram model (Should take 5-10 minutes)