From: Jacob Fugal <lukfugl@...>
Date: 2005-07-17T00:46:57+09:00
Subject: Re: [QUIZ] Sampling (#39)

On 7/16/05, Olaf Klischat <klischat@cs.tu-berlin.de> wrote:
> > ezra:~/Sites ez$ head big_sample.txt
> > 168
> > 285
> > 566
> > 604
> > 912
> > 1183
> > 1335
> > 1473
> > 1728
> > 1919
> > ezra:~/Sites ez$ tail big_sample.txt
> > 999998155
> > 999998313
> > 999998484
> > 999998680
> > 999998825
> > 999999151
> > 999999330
> > 999999465
> > 999999621
> > 999999877
> > ezra:~/Sites ez$
> 
> Umm... I'm not sure, but that looks a bit too "equidistant" to be
> truly random, doesn't it?
> 
> The sample being truly random means that the sample should be a truly
> "drawing without putting back" (e.g. lottery) sample, so each possible
> sample occurs with equal probability. So a sample like
> 
> 0
> 1
> 2
> ..
> ..
> ..
> 4999999
> 
> should occur with the same probability as any other more "likely" one.

See my other posts in this thread about the actual probabilities. In
short, since it's fully random, each possible sampling is as likely as
any other possible sampling, but the number of samplings including at
least ten numbers in the 99999xxxx range and at least ten numbers in
the (00000)xxxx range is *much* higher than the number of samplings
without numbers in those ranges. So the probability of getting a
sampling that looks evenly spread out is much more likely than getting
a sampling that's clustered.

Jacob Fugal