Date: Thu, 05 Oct 95 13:14:56 -0400
From: [Permission pending]
To: rusin@math.niu.edu
Subject: strong and weak laws

Hello,
I have visited your web page where you have mentioned that you like challenges.
This is not a theoretical rather a pedagogical challenge with which I have been
struggling for quite a while. In fact if you can believe Feynmann, then one
does not quite understand the subject until one can explain it in plain common
language. Well, here it is: explain the difference to a layman between the weak
and strong laws of large numbers. When I taught probability theory to first
year graduate students in electrical engineering (communications and signal
processing) and was asked this question I failed completely. The students do
not know measure theory, or the concept of almost everywhere, etc. Do you a
have a good suggestion? How would you explain it to your wife or mother, is it
possible at all? 

Cheers
[Permission pending]

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Date: Fri, 13 Oct 95 12:57:53 CDT
From: rusin (Dave Rusin)
To: rusin
Subject: strong and weak laws

[For some reason  a cc: to myself did not return -- 10/11/95. Basic ideas:]

[Disclaimer - not a statistician. Gut understanding follows]

Consider lots of people flipping coins. Weak law: as time goes on, fewer and
fewer people should be flipping, say, 60% heads.

But potentially, this could happen by having each person flip mostly
50-50, except that everyone keeps having long enough runs of heads so
as to get their average to 60%. By the previous paragraph, this would
have to happen with greater and greater pauses between their 60% moments,
but it could happen.

Strong law says this really _cannot_ happen.