Problem 1. In class we gave the following equation for the bigram probability of a sequence of words Wu), ..., wc): k Pr(W(1), W\") = H Pr{W{\"|W("1) = anti-1)) (1) Using this formula, give an expression for the bigram probability of the sentence abab, where each character is treated as a word. 'D'y to simplify the formula as much as possible. Problem 2. Let us suppose that there are two possible symbols [words in our language, a and b. There are three conditional distributions in the bigram model for this language, Pr(W(i)|W(_1l = a),Pr(W(i)IW(i_1) = b), and Pr(W(")[W{'-_1) = start), where start is the start symbol which begins any sentence. These conditional distributions are associated with the parameter vectors 6,], I95, and 35m\