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I encountered the problem here(Hidden Markov Chain)

It is like this:

The task is to compute, given the parameters of the model, the probability of a particular output sequence(observed sequence). This requires summation over all possible state sequences: The probability of observing a sequence(output sequence)

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of length L is given by

enter image description here (*)

where the sum runs over all possible hidden-node sequences

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For more specific information on the related information, refer to here

My problem is:

How the (*) equation can be derived?

It seems to be according to Total Probability Theorem. But this does not make sense to me.

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    Does $P(Y) = \sum_X P(Y \; X) $ makes sense to you?2011-09-27

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