Consider the HMM shown in the figure below (Figure 1). Let the set of output states be U = {g, h, i} and the set of hidden states be {1, 2, 3) where 3 is the stop state (you may also consider 0 as the start state). 7, A & B represent initial, transition and emission distribution parameters of the model. You are tasked to find these parameters using the data given below by answering the questions that follow. Y-1 X-1 Y X Figure 1: Bayesian Network for Question 1 The dataset (D) contains 4 sequence pairs, which are independent and identically dis- tributed. These pairs are generated from the same aforementioned probabilistic graphical model (HMM). Each pair contains a sequence of outputs and a corresponding sequence of hidden states. D = {"g/1 h/2", "1/2", "g/2 i/1", "g/1 i/1"} (a) State the likelihood equation (P(D|0)) for the data in terms of initial (7), transition (aj), and emission probabilities (b; (o)). (2 points) (b) State the maximum likelihood estimates for all possible aj and b; (o) given the data (D). (4 points)