Assigned: Feb. 26
Due: Mar 5
Prob(P) = 0.8 Prob(C) = 0.19 Prob(H) = 0.01 Prob(K | P) = 0.1 Prob(K | C) = 0.2 Prob(K | H) = 1.0.A. Evaluate Prob(P | K), Prob(C | K), and Prob(H | K).
B. I check my pockets again, and again don't find the keys. Suppose that the two checks of my pockets are independent and identical. That is, let M be the event that I will miss my keys twice in checking the pocket twice. We suppose that
Prob(M | P) = (Prob(K | P))2 = 0.01 Prob(M | C) = (Prob(K | C))2 = 0.04 Prob(M | H) = (Prob(M | H))2 = 1.0.Evaluate Prob(P | M), Prob(C | M), and Prob(H | M).
C. Estimate how many times I have to check my pockets before I am 90% sure that I have left my keys at home.
A. Give an example to show that
P(Tag=noun | Tag=verb, Tag=conjunction)
is not zero. (All I'm asking for is one sentence with those three elements in a row.)
B. Propose a method that will allow you to combine probablistic information from the trigram model with syntactic constraints. Explain how this would fix this problem.