Random numbers?
Mark Spahn
The Jumble that appears on February 14, 2006 is illustrated by a
cartoon in which a math teacher at a blackboard is adding up
the following eight 8-digit numbers:
72386289
87627136
37829263
68272418
37928123
26137267
38248372
73461297
(The sum, incidentally, is 441,890,165.)
When people extemporaneously try to come up with random digits,
they often generate patterns that a true random number generator
would not generate. Did something like that happen here?
Can we decide, from the above 64 digits, whether they came
from a random number generator, or were rather djinned up
by a human? For what it is worth, the above 64 digits consist of
0 0's, 5 1's, 14 2's, 10 3's, 3 4's, 0 5's, 8 6's, 11 7's, 9 8's, 4 9's.
How random is this sequence of 64 digits?
Does the question even make sense?
-- Mark Spahn
Proginoskes
Not too random. With 64 random digits, you would expect "double digits"
(the same digit twice) 10% of the time. The fact that there are no
double digits (reading across, rows left to right) means they were
probably human-generated.
> Does the question even make sense?
Yes. You can ask questions like what is the expected number of 1's,
what the standard deviation of the number of 1s is, etc.
--- Christopher Heckman
Jasen Betts
not very random. there's a statistical test for conformance of discrete
distributions to an ideal (I'm assuming the ideal here would be 6.4 of each
digit :) )
that being the case probability of getting 0 5's and 0 1's is extremely
low.
Bye.
Jasen
Henning Sudbrock
> When people extemporaneously try to come up with random digits,
> they often generate patterns that a true random number generator
> would not generate.
There are no patterns that a true random generator would not generate. A
true random number generator would generate each sequence with exactly
the same probability. So given some sequence it could always be
generated by such a random number generator.
>Did something like that happen here?
> Can we decide, from the above 64 digits, whether they came
> from a random number generator, or were rather djinned up
> by a human? For what it is worth, the above 64 digits consist of
> 0 0's, 5 1's, 14 2's, 10 3's, 3 4's, 0 5's, 8 6's, 11 7's, 9 8's, 4 9's.
> How random is this sequence of 64 digits?
This sequence is as random as any other sequence.
> Does the question even make sense?
I guess that one can ask how probable it is that some sequence was
generated by a human being, but this is not a mathematical question, but
rather a question for other sciences (sociology, psychology,
anthropology (?) ).
This question would be: "Is a human being a true random number generator?"
That means: Is his choice of each new number independent of the numbers
he chose before. My guess is that the answer is no ;)
--Henning
Stig Holmquist
wrote:
It seems to me that one should be able to calculate the
number of voids, single, pairs, trips, quads etc amongst
64 random digits and then apply the chi-squared goodness-
of-fit formula. But perhaps the "cells" are too small.
Stig Holmquist
Christopher
> 72386289
> 87627136
> 37829263
> 68272418
> 37928123
> 26137267
> 38248372
> 73461297
>
> they often generate patterns that a true random number generator
> would not generate. Did something like that happen here?
In a random sequence of 64 digits, the probability that a single digit
appears 0 times is 10 * (9/10)^64 = 0.0118. The probability that *two*
digits appear 0 times is 10C2 * (8/10)^64 = 0.000028. The probability
of this happening *and* there being no doubles is 10C2 * 8/10 *
(7/10)^63 = 0.0000000049.
In order to come to a rigorous conclusion, you would have to list the
errors humans make when trying to generate random sequences. Obviously
if the list was long enough, then even most randomly-generated
sequences would match *something* on the list. But if it was a
relatively short list, and "missing digits" and "missing repeats" were
on it, then it looks like this sequence would have statistically
significant evidence for being human-generated.