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bowlbase
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Homework Statement
Consider an HMM with two possible states, “R” and “G” (for “regulatory” and “gene” sequences respectively). Each state emits one character, chosen from the alphabet {A,C,G,T}.
The transition probabilities of this HMM are:
aRG = aGR = 1/4
aRR = aGG = 3/4
The emission probabilities are:
eR (A)= eR (C)= eR (G)= eR (T)=1/4
eG (A)= eG (T)=2/10 and
eG (C)= eG (G)=3/10
Assume that the initial state of the HMM is “R” or “G” with equal probabilities. Given a sequence S = ACGT and an HMM path π = RGGR, calculate the probability Pr(S, π) of the sequence and the path.
Homework Equations
$$P(S,\pi) = \prod_{i=1} a_{\pi_{i-1}},\pi_i e_{\pi_i}(x_i)$$
The Attempt at a Solution
We discussed this equation in class but never actually used it or spent time describing how to wield it. I just don't see how the information I'm given comes together in that equation.
Thanks for any help.