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Consider the HMM shown below: Xo X1 X2) EL E2 The prior probability P(Xo), dynamics model P(X++1 | Xt), and sensor model P(Et | Xt) are as follows. Et X+ P(Et|Xt) Xt+1 X+ P(X++1|Xt) a 0 0.3 x. P(X) 0 0.3 b 0.15 0 0.2 1 0 0.7 c 0 0.55 1 0.8 0 1 0.05 a 1 0.1 1 1 0.95 b 1 0.45 1 0.45 Q5. Hidden Markov Models: The Forward Algorithm (20 points) E2 = c. What is the updated belief Consider the same HMM as Q4. We have evidences E1 B2(X) = P(X2 | Ej = c, E2 = c)? Consider the HMM shown below: Xo X1 X2) EL E2 The prior probability P(Xo), dynamics model P(X++1 | Xt), and sensor model P(Et | Xt) are as follows. Et X+ P(Et|Xt) Xt+1 X+ P(X++1|Xt) a 0 0.3 x. P(X) 0 0.3 b 0.15 0 0.2 1 0 0.7 c 0 0.55 1 0.8 0 1 0.05 a 1 0.1 1 1 0.95 b 1 0.45 1 0.45 Q5. Hidden Markov Models: The Forward Algorithm (20 points) E2 = c. What is the updated belief Consider the same HMM as Q4. We have evidences E1 B2(X) = P(X2 | Ej = c, E2 = c)