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Subject: Re: Waltzing Matilda (was: statistics, 10 events tell us what ?

Author: Dan Homan

Date: 07:17:11 08/17/98

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It seemed clear to me that you defined the trials as separate units, on
re-reading I see that "20 in a row" could stretch across trials.  If
you would like to work out this case, let me know the answer.

You asked me to reconsider my answer for (c), but I didn't answer (c).
In c) it is quite ambiguous what you meant by "the chance this result does
not contradict the fair coin hypothesis", so I simply gave you the
probability of getting 4 trials of "20 in a row" in an N-trial experiment.
My "off-my-head" statistics knowledge is not good enough to answer such
an ill-posed question - so I gave you the best information that I could...
please let me know the final result.

In (d) I simply set the dispersion of a N-trial result equal to 1 and solved
for N.  This is a ball-park figure, I know, but it was the best I could
do sitting at the computer screen.  If you have a better result, please
let me know.

This was obviously more of an exercise in word games than statistics.
I'm not sure what point you are making, except the obvious one that these
questions need to be well defined or we will all talk right past one
another.

 - Dan

P.S.  Here is an interesting story about physists and mathematicians....

There was a famous physist (I can't remember his name) who claimed to be
able to tell a physist from a mathematician by how they answered the
following question:

  Two brothers live 10 miles apart.  They both leave their houses one day,
  at the same time, and walk on a straight line towards one another.  Each
  brother is walking at 4 miles an hour.  One brother has a dog who leaves
  his house with him.  The dog is running at 8 miles an hour.  When the dog
  reaches the other brother, he turns around and goes back to his owner.
  When he reaches his owner, he turns around again towards the other brother.
  The dog keeps up this back and forth travel between the brothers until they
  meet.  How far has the dog traveled?

The fellow found that physists will reply with the correct answer instantly,
while mathematicians will take several minutes to sum the series before
giving the correct answer.  He found this to be an excellent descriminator
between physists and mathematicians.  One day, this famous physist met the
reknown mathematician, Jon Von Neumann, to whom he posed this question.  Von
Neuman replied instantly, which surprised the physist.  He asked Von Neumann,
"But you are a mathematician, I was sure you would sum the series."
To which, Von Neumann replied, "I did."

Here is another one:

A physist, mathematician, and engineer are given the challenge of enclosing
the most area with the shortest length of fence.  The engineer promptly
forms a circle, stating that it is the most efficient solution.  The physist
takes the fence and starts making a straight line toward the horizion
while mumbling something about one infinity being larger than another.
The mathematician thinks for a moment and then makes a very tight circle of
fence around himself and states, "I define myself to be in the outside!".




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