2. (40 points) The following is the first paragraph of Ernest Hemmingway's The Old Man and The Sea. It has been POS-tagged using the online Brill tagger at the Center for Sprogteknologi at Kobenhavns Universitet. A few minor changes have been applied PRP VBD DT JJ NN WP VBD RB IN DT NN IN DT NNP NNP CC PRP VBD VBN CD NNS RB IN VBG DT NN he was an old man who fished alone in a skiff in the gulf stream and he had gone eighty-four days now without taking a fish . IN DT JJ CD NNS DT NN VBD VBN IN PRP . CC IN CD NNS IN DT NN DT NN POS NNS VBD VBN PRP IN DT in the first forty days a boy had been with him . but after forty days without a fish the boy 's parents had told him that the JJ NN VBD RB RE CC RB VBN , WDT V VBZ DT JJ NN IN JJ , CC DT NN VBD VBN IN PRP$ NNS IN old man was now definitely and finally salao , which is the worst form of unluck , and the boy had gone at their orders in NN WDT VBD CD JJ NN DT JJ NN . PRP VBD DT NN JJ TO VB DT JJ NN VB IN DT NN IN PRP$ another boat which caught three good fish the first week . it made the boy sad to see the old man come in each day with his NN JJ CC PRP RB VBD IN TO VB PRP VB DT DT VBD NNS CC DT NN CC NN CC DT NN WDT VBD skiff empty and he always went down to help him carry either the coiled lines or the gaff and harpoon and the sail that was VBD IN DT NN . DT NN VBD VBN IN NN S CC , VBD , PRP VBD IN DT NN IN JJ INN furled around the mast . the sail was patched with flour sacks and , furled , it looked like the flag of permanent defeat . This assignment does not require programming, but if you wish to work with an electronic version of this information, you can refer to the following file (this file is also available on Canvas): /dropbox/21-22/473/assignment3/old-man. txt Hint: you can refer to lecture 4 and lecture 5. a. How many bigrams does the sample contain? b. In a bigram model, we assume that the POS tag of the current word depends only on the POS tag of the preceding word. Calculate P(. | NN), assuming that the counts in the above sample are perfectly representative. Note that, "." in P(. | NN) is a POS tag (i.e., the POS tag of a period). C. We are interested in the probability of the bigram DT JJ in the sample text. What is the value of P(DT JJ)? d. A trigram model predicates a POS tag on the POS tags of the preceding bigram. Calculate P(NN | DT JJ) for the sample. . Assume this sample characterizes a larger corpus. Estimate P(DT JJ | NN) for the corpus. Hint: this will use Bayes' Theorem