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Re: Geiger (a challenge)



At 09:03 AM 7/8/00 -0400, Ludwik Kowalski wrote:

The exponential distribution [of Geiger-counter interpulse times]
may be counter-intuitive.
Knowing that the distribution of counts per unit time
is Gaussian (or Poissonian, to be more general) many
of us would expect a bell-shaped distribution of dt.
For example, at the average counting rate of 5 counts per
second one may expect that distribution to be symmetrical
about the mean time of 0.2 seconds.

Would one really expect that? I always thought radioactive decay events
were IID (that is, Independent and Identically Distributed). If they're
IID, then the probability of one _not_ happening over a stretch of time
must be an exponential function of time.

The fallacy of expecting the spacings to be clustered around the mean
spacing is equivalent to the well-known fallacy that alleges if a family
already has five daughters and is expecting another child, it must be a boy
with very high probability, to uphold "the law of averages".

In fact, of course, births are IID to a good approximation.

For related fallacy, see next message.

The experiment contradicts such expectations.

I should hope so!

It is tricky experiment to setup.

There's no reason for it to be tricky. There's no reason to use a lot of
software and hardware (including radioactive sources) that most people
don't have (and might not want) in their classroom. You could make this
point to sixth-graders using dice. How long a run can we have, rolling one
die, before a six shows up? What does the histogram of run-lengths look like?

Warning: To get good statistics you'd need hundreds of runs, which means
thousands of dice-rolls. If you can provide one die per student, you can
parallelize the data collection.

If you like, you can use a computer to roll the dice for you.
a) You can do the entire job using nothing but excel. Hint: if the Data
Analysis option isn't showing on the Tools menu, use Tools::Add-Ins to load
the Analysis package. That's where the histogram tool lives. (Don't
expect the chart tool to take raw data and histogram it; you have to form
the histogram first, then chart it.)
b) OTOH it is probably easier to do (and easier to understand) if you
write a Basic program to roll the dice and form the histogram; then print
out the data and chart it using excel.

Huge hint: If you have excel on your computer, you don't need to buy a
Basic programming system. There's a perfectly fine Basic engine hiding
inside excel. For excel version 9 ("excel 2000") it's hiding under
Tools::Macro::VisualBasicEditor. It's there in earlier versions but I
forget where it hides; use the "help" function and look for the word "module".