(50%) Based on the information given in the tables below, answer the following questions. Unigram Information 5000 386 980 65 24 197 115 170 62 31 at the nine o'clock she worked in university of Macau principal 1 4 Bigram Information at she at nine nine o'clock she worked worked in in the the university university of of Macau 383 86 5 2 2 11 10 1 54 0 (a) (20%) Calculate bigram probabilities for the sentences "At nine o'clock" and "She worked in the University of Macau". (b) (20%) Apply Add-a smoothing technique and re-calculate bigram probabilities for each sentence in (a). Let a = 1 and vocabulary size = 1000. (c) (10%) Calculate the perplexity for each of these probabilities based on the results in (b).