Consider an HMM with an explicit final state w₀, and a unique visible symbol v₀ for w₀. The transition probabilities are provided below along with emission probabilities. Assume that the index begins at 0 for the matrices.

aij =

1	0	0	0
0.2	0.3	0.1	0.4
0.2	0.5	0.2	0.1
0.8	0.1	0.0	0.1

bjk =

1	0	0	0	0
0	0.3	0.4	0.1	0.2
0	0.1	0.1	0.7	0.1
0	0.5	0.2	0.1	0.2

a. What is the most likely state sequence that generated v⁴ = {v₁, v₃, v₂, v₀}? Use HMM forward algorithm.

b. Given v⁴, what is the most likely sequence of hidden states?