Suppose I have a random event with k possible outcomes of equal probability. What distribution (if any) describes the probability of obtaining a specific sequence of length m after n events?
@faelif see here: https://d1wqtxts1xzle7.cloudfront.net/48627809/Perceptions_of_randomness_why_three_head20160906-24058-r0pr5l-libre.pdf and Ross (2007) Introduction to Probability Models. ch. 4
Thanks, I'll take a read
the probability of observing a single specific sequence is (1/k)^m.
E.g. if you are flipping a fair coin then p(h)=p(t) = 0.5 (k==2). The probability of observing some specific sequence htththhthtis just 0.5^m where here m = 10.
The question is about finding the sequence in a larger string, though - for example, HHTTH contains TH
See also here:
https://mathstodon.xyz/@faelif/114304154631186813
@faelif @jerlich Jeff is confusing the probability of a sequence of length m occurring in n flips of a coin where m=n with that probability when n > m (ie ocurrence as a subsequence). Subsequence probabilities are not equal across sequences. The references I gave are precisely about that! https://d1wqtxts1xzle7.cloudfront.net/48627809/Perceptions_of_randomness_why_three_head20160906-24058-r0pr5l-libre.pdf
@jerlich @faelif what are k and m? the number of outcomes and the sequence length? because if yes that is answering a less general question than the one asked