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Hope you can give me an answer regarding this trellis diagram. why in this picture of a general first-order markov chain of 2 states,we should know the prob. of each state at each time?

A general first-order markov chain, can be Time-dependent(non stationary) so Transition prob. can change by time. That's why we have E(time) in the picture. but by having the initial Prob. of each state (P(t=1)), and Transition prob. i can calculate prob. of each state in any given time, so The state probabilities at each time (P(t=2,t=3,...)) are Extra informations. am i right or i ignore something?

pic.Statistics in Volcanology (google books) page 167 MArkov chain

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# General first-order markov chain of 2 states

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