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I'm working on a problem to find the expected frequency of a pattern. Say there is a sequence of alphabets - A, B, C and D.

The sequence is: ABDACDBADA.

I want to find the expected frequency of a pattern ACD given the sequence above. So I calculated the frequencies of A (0.4), B(0.2), C(0.1) and D(0.3) separately.

Initially I thought, multiplying the frequencies of A, C and D would suffice, i.e., 0.4 * 0.1 * 0.3 = 0.012. But, this is not what i need as I need to conserve the order of ACD.

Can anyone tell me how to proceed with this?

Thanks!!

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    The question is not at all clear. What do you mean by "the expected frequency of a pattern ACD given the sequence above"? The frequency in what? In the given sequence? Is there supposed to be some random process occurring here?2012-08-27
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    In the sequence I mentioned "ABD'ACD'BADA", the pattern occurs only once. This I could probably say is the observed frequency. Now by learning the individual frequencies of each alphabet from the sequence, I want to know what is the expected frequency of the pattern ACD in the given sequence.2012-08-27
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    Basically, to make it short I just need know to the probability of the pattern, 'ACD' from the given frequencies of each alphabet.2012-08-27

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