(Solved):   A simple hidden Markov model. A two-state hidden Markov model (HMM) describing DNA sequenc ...

 

A simple hidden Markov model. A two-state hidden Markov model (HMM) describing DNA sequence with a heterogeneous base composition is shown in the following figure: (a) State 1 generates AT-rich sequence, and state 2 generates CG-rich sequence. State transitions and their associated probabilities are indicated by arrows, and symbol emission probabilities for \( \mathrm{A}, \mathrm{C}, \mathrm{G} \) and \( \mathrm{T} \) for each state are indicated below the states. The initial probabilities of state 1 and 2 are \( 0.55 \) and \( 0.45 \) respectively. Evaluate the probability of an observed sequence "ATCG" in a human DNA-profile using Forward algorithm.