2. To better understand the HMM underlying the protein family application consider the following (much smaller scale) model: The states and their transition probabilities are 0.2 depicted on the right. There are three classes of states: rectangles, circles and hexagons. Each C emit different symbols with different frequent 0.3 0.25 cies. Rectangles will emit the symbols 1, 2, 3 0.5 with equal probabilities, hexagons emit a 2 with 0.5 A1 A2 probability 0.4 and a 4 with probability 0.6, cir- cles are equally likely to emit 0 or 4. 0.25 0.7 Every process starts in state Al and ends in A2. B That is, both Al and A2 emit a single symbol only. 0.3 (a) Carefully define the state space S and the emission alphabet A for this example. Explicitly write down the parameters 1 = (7, P, B). (b) Let q denote a state path and O a vector of observations. Explain, why argmax P(q|0, )) = argmax P(q, Old) (c) For q = (91, . . ., 95) and O = (3, 0, 4, 2, 1) find argmax P(q|0, A). For this state path, find P(q O, A)