I used a brute force method to check the probability. Counted the number
of triples in 600 random numbers 0-9, repeated that 10000 times and took
the mean: 5.99
So it looks like Chris's number is more accurate.
Benedict
Op 6/12/2022 om 09:25 schreef Alex Prengère:
@Chris Indeed the true figure, if my math is correct, is a bit under
5.98 because of the "non-independence" of triplets.
I computed it and found 5.382, so finding 6 is entirely normal.
For the details: calling L = 600 and n = 3
* number of possible sequence of L digits: 10^L
* if a specific digit appears in a specific position n times, the rest
of the sequence has 9*10^(L-n-1) possibilities [9 because after the
repetition you have a different digit]
* we need to multiply that number by 10 as we have 10 digits
* we need to multiply it again by L-n+1 as the digit can start in
any place until the L-n+1 place
* so the total number of sequence of L digits with at least 1
repetition of length n is: 9*10^(L-n-1) * 10 * (L-n+1)
Dividing the 2 to compute the probability:
P = 9*10^(L-n-1) * 10 * (L-n+1) / 10^L = 9*10^(L-n) * (L-n+1) / 10^L
$ python3 -c "L = 600; n = 3; print(9*10**(L-n) * (L-n+1) / 10**L)"
5.382
Regards,
Alex
Le mar. 6 déc. 2022 à 07:34, Greg Ewing <gcew...@snap.net.nz
<mailto:gcew...@snap.net.nz>> a écrit :
On 6/12/22 3:58 pm, James Johnson wrote:
> I came back to this thread looking for the list of randomness
tests, and
> I keep missing them somehow.
If you're interested in testing a PRNG really thoroughly, check
out TestU01:
http://simul.iro.umontreal.ca/testu01/tu01.html
<http://simul.iro.umontreal.ca/testu01/tu01.html>
--
Greg
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