If I have a markov chain transition matrix for 2 states. Specifically in my case, it is a transition matrix for a bacterial genome with 4 random variables being A,C,G and T. (The bases) If I want to calculate the probability of a random sequence like GATTACA occurring from the markov chain, how would I go about it?
I was thinking that I would have to do it by :
P(A|G) * P(T|A) * P(T|T) * P(A|T) * P(C|A) * P(A|C)
But I am not sure what to do with the first G. Do I take its probability as 1 or do I use the stationary distribution of transition matrix value for G?