- #1
dabd
- 25
- 0
Hi,
I have the following probability question:
Given a random bit string S of length m, if I take a copy of a proper suffix of S (a suffix of S that is neither equal to S, nor empty), and align it with the start of the string, how many consecutive matches starting from the beginning of the string do I expect to see on average?
For example:
Given
S[1..9] = 101010110
If I take the suffix starting from position 3: S[3..9] = 1010110
and align it with S:
S[1..9] = 101010110
S[3..9] = 1010110
How many consecutive matches on average starting from position 1 do I expect to see?
My guess is that since for each position the probability that a symbol matches another is 1/2, half of the sequence would be matches, but I am not sure of this since this line of thought doesn't take in account the consecutive ordering of the sequence of matches.
Can someone please enlighten me?
Thanks.
I have the following probability question:
Given a random bit string S of length m, if I take a copy of a proper suffix of S (a suffix of S that is neither equal to S, nor empty), and align it with the start of the string, how many consecutive matches starting from the beginning of the string do I expect to see on average?
For example:
Given
S[1..9] = 101010110
If I take the suffix starting from position 3: S[3..9] = 1010110
and align it with S:
S[1..9] = 101010110
S[3..9] = 1010110
How many consecutive matches on average starting from position 1 do I expect to see?
My guess is that since for each position the probability that a symbol matches another is 1/2, half of the sequence would be matches, but I am not sure of this since this line of thought doesn't take in account the consecutive ordering of the sequence of matches.
Can someone please enlighten me?
Thanks.