A DNA sequence is a series of components from {A, C, G,T}. Now let's assume there is one hidden variable S that controls the generation of DNA sequence. S takes 2 possible states {S1, S2}. Assume the following transition probabilities for HMM M: P(SIS) = 0.75, P(S2|SI) = 0.25, P(SS2) = 0.25, P(S2|S2) = 0.75 emission probabilities as following: P(A|S.) = 0.4, P(C|S.) = 0.1, PG|S.) = 0.4, P(T|S) = 0.1 P(A|S2) = 0.1, P(C|S2) = 0.4, P(G|S2) = 0.1, P(T|S2) = 0.4 and start probabilities as following P(SI) = 0.5, P(S2) = 0.5 Assume the observed sequence is x = CGTCAG, calculate PGM) using the forward algorithm. Draw the HMM, and show your work to get full credit