Consider an ergodic 4-state Hidden Markov Model (HMM) dened over a discrete set of ve symbols, with tran- sition matrix A, emission matrix B and...

The question is as below. How to solve this problem? Thank you!

Consider an ergodic 4-state Hidden Markov Model (HMM) defined over a discrete set of five symbols, with tran-sition matrix A, emission matrix B and initial state vector 1r, defined as: 0.1 0.3 0.3 0.30.7 0.1 0.1 0.1 A: 0.25 0.25 0.25 0.250.1 0.4 0.4 0.10.6 0.1 0.1 0.1 0.1B_ 0.1 0.6 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.20 0 0 0.5 0.5 «=[025 0.25 0.25 0.25] In the transition matrix, columns indicate previous state, and rows indicate current state. For instance, a transitionfrom state 2 to state 3 has probability of 0.1. (a) What is the probability p(Q) of the state sequence Q = [1234]? (b) What is the probability p(Q,O) of the combined state and observation sequence Q : [1234] and O : [5321]?What is the probability for the same state sequence but observation sequence 0 = [5324]? (c) What is the average duration in each of the model states?