From: Jacob Fugal <lukfugl@...>
Date: 2005-07-16T04:54:52+09:00
Subject: Re: [QUIZ] Sampling (#39)

On 7/15/05, Cassio Pennachin <pennachin@gmail.com> wrote:
> > Shouldn't those number be more like
> >
> >   999999xxx
> 
> As far as I know, they just have to be between 0 and LIMIT-1.  In
> fact, if the tail end of the sample is heavily concentrated as you
> suggest, it's probably a badly biased sample.  Unfortunately, my
> sampler is biased as well, just not in this particular way.
> 
> It's not hard to remove the bias, but then the script would be 50-60%
> slower, which makes it significantly less useful for taunting others
> ;-).

Probability of a random sample X from population (0...1_000_000_000)
being less than or equal to 462_470_382 is 0.462470382. Probability of
ALL 5_000_000 random samples from same population being less than or
equal to 462_470_382 is (0.462470382 ^ 5_000_000) < 1.0e-1_674_580.
Those are VERY slim chances. Additionally, that figure assumes repeats
are allowed. Since they're not, after each sample below 462_470_382,
it will be even LESS likely that the next sample will also be below
462_470_382 since there are fewer low numbers to choose from. I
wouldn't be surprised if the actual chance were less than
1.0e-2_000_000. It IS possible, but not likely.

Now on the other hand, the probability of the last number being >=
999_999_000 is the probability of ANY being >= 999_999_000 which is
exactly the same as the negation of the probability that ALL are <
999_999_000. Using the same procedure as above, that probability is
(0.999999 ^ 5_000_000) == 0.006738. So the probability of ANY of the
samples being at least 999_999_000 is (1.0 - 0.006738) = 0.993262, or
99.3262%. Pretty good chances.

Jacob Fugal