From: Jacob Fugal <lukfugl@...>
Date: 2005-07-16T05:07:03+09:00
Subject: Re: [QUIZ] Sampling (#39)

On 7/15/05, Cassio Pennachin <pennachin@gmail.com> wrote:
> > I think Jim's point was that if your last digit is 462470382 then you
> > don't have a random sample...
> 
> If by definition a random sample has to be uniform over the
> range/population it samples, you  are correct.  Although even by such
> definition it's possible that the last number would be this low in a
> uniform sampling, the odds are very low.  And I know that my script
> doesn't uniformly sample the range, as I said before.  I coded it to
> be fast yet still meet the letter of the requirements.

We can concede this. I still believe that the *spirit* of the
requirements was a Uniform Random Distribution.

> ... and neither is any algorithm that
> frequently generates 999999xxx for the last several entries.

This statement I contest. I showed in my other post that the
probability the last number is 999999xxx is greater than 99%.
Expanding that calculation (I can show the work upon request) the
probability all the last ten numbers being 999999xxx is 93.5%. Getting
small enough that you'll see some 999998xxx numbers in the last ten
every now and then, but still quite likely. Chances that you'll see a
999997xxx number in the last ten: 0.05% (about once out of every 2000
trials)

Jacob Fugal