1. 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 M 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 A, C, G and 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. 0.99 1 A 0.4 C G T 0.1 0.1 0.4 0.01 0.1 2 A 0.05 C 0.4 G 0.5 T 0.05 0.9 information that 95% of sick [C