Problem 1: Viterbi Decoding Observation Likelihoods (B array) VB State Transition Probabilities (A array) VB NN PRP PRPS JJ 0.15 0.5 0.2 0.05 0.05 0.0001 0.2 0.005 0.004 0.002 NN 0.05 0.002 0.002 0.001 PRP 0.25 0.05 0.001 0.001 0.01 PRPS 0.25 0.1 0.001 0.001 0.05 JJ 0.0001 0.2 0.05 0.001 0.05 Dumbledore 0 0 VB NN 0.01 fed 0.10 0 0 0 0 his phoenix peanuts 0 0 0 0 0.2 0.10 0.15 0 0 0.10 0 0 0 0.05 0 PRP PRPS JJ 0.1 0 0 (a) Using the matrices given, compute by hand the Viterbi trellis (as shown in Figures 6.10 and 6.12) and backpointer matrix (as used in Figure 6.11) for the sentence Dumbledore fed his phoenix peanuts". (b) What is the most likely sequence of tags? Problem 2: Forward Algorithm. (a) Using the matrices given in problem 1, compute by hand the forward path probability trellis for the sentence "Dumbledore fed his phoenix peanuts". (b) What is the probability of the sentence