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)IW('_1) = o),Pr[W(i)|W(i_1) = b), and Pr(W(")IW{'__1) = start}, where start is the start symbol which begins any sentence. These conditional distributions are associated with the parameter vectors 9,], 195, and 35mm respectively (these parameter vectors were imphcit in the previous problem). For the current problem, we will assume that these parameters are xed. Suppose that we are given a sentence W\"), ...,W\"']. We will use the notation 11:4,, to denote the number of times that the symbol 3; occurs immediately following the symbol a? in the sentence. For example, ung counts the number of times that symbol (1 occurs immediately following the symbol a. Using Equation 1, give an expression for the probability of a sentence in our language: PT(W(I]1"'1W(k)lsar55stnrt) (2) The expression should make use of the fix)3; notation dened above. (Hint: the expres- sion should be analogous to the formula that we found for the likelihood of a corpus under a bag of words model.)