Testing random
Ned Batchelder
ned at nedbatchelder.com
Sun Jun 7 17:21:48 EDT 2015
On Sunday, June 7, 2015 at 2:26:02 PM UTC-4, Thomas 'PointedEars' Lahn wrote:
> Chris Angelico wrote:
>
> > On Mon, Jun 8, 2015 at 2:36 AM, Thomas 'PointedEars' Lahn
> > <PointedEars at web.de> wrote:
> >>> The greater the multiplier, the lower the chance that any element will
> >>> have no hits.
> >> Wrong.
> >>
> >>> [ex falso quodlibet]
> >
> > Huh. Do you want to explain how, mathematically, I am wrong, or do you
> > want to join the RUE in my ignore list?
>
> I already did; you have overlooked it. In a nutshell, the probability of
>
> 1 1 1 1 1 1 1 1 1 1 1
>
> is *the same* as that of
>
> 1 2 3 4 5 6 7 8 9 1 2
>
> and the same as that of
>
> 8 3 6 3 1 2 6 8 2 1 6.
>
You aren't agreeing because you are arguing about different things.
Thomas is talking about the relative probability of sequences of digits.
Chris is talking about the probability of a single digit never appearing
in the output.
Thomas: let's say I generate streams of N digits drawn randomly from 0-9.
I then consider the probability of a zero *never appearing once* in my
stream. Let's call that P(N). Do you agree that as N increases, P(N)
decreases?
--Ned.
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