Re: Central Limit Theorem

["John S. Denker" <jsd@MONMOUTH.COM>]

Ludwik Kowalski wrote:
>
> Where is a connection between the corn pop sound and the
> central limit theorem?

I'm with Ludwik on this one!  Asking whether corn-popping illustrates the
central limit theorem seems analogous to asking whether eagles fly around
in caves.  The answer is no, not normally, and there are about 5 reasons
why you shouldn't try it, and even if you force the issue it doesn't tell
you much about caves or eagles or corn or the central-limit theorem.

Then at 10:20 AM 12/18/99 -0600, Carl C. Gaither wrote:
> I interpreted the quote to suggest that you start with no sounds of any
> corn popping, then as the corn starts popping the noices increases to a
> maximum and finally as there is less and less corn to pop the noise
> decreases until finally there is no more sound of corn popping.
> increases in inten

No, that interpretation does not come close to satisfying the premises of
the central limit theorem.  The CLT has to do with sampling
identically-distributed events with different sample sizes.  The ramp-up
and ramp-down of the popping rate has to do with a grossly nonstationary
process i.e. grossly non-identically-distributed events.

------

I don't understand the purpose of even asking the question.
  a) I understand that it is sometimes good to ask open-ended questions, and
  b) I understand that it is important to emphasize that theorems have
premises as well as conclusions (if the premises don't hold then you can't
conclude the conclusion).

... but combining (a) and (b) seems like poor pedagogy.  Teaching point (b)
IMHO needs to be done under carefully controlled conditions.  The
corn-popping question as stated seems like a booby trap, practically
begging people to misapply the theorem.