Re: Geiger, not binomial ?

[John Denker <jsd@MONMOUTH.COM>]

> "Glenn A. Carlson" wrote:
>
> > There is every reason to expect your data to fit a binomial
> > distribution since it is the correct distribution.

Right.

> However, as Mr.
> > Cleyet correctly points out, the Poisson distribution is more useful
> > here because of the huge number of nuclei in your sample (on the
> > order of 10^23) and the virtually zero probability that any one
> > nucleus will decay during the counting interval.  ....

Exactly right, again.

Then at 06:50 PM 3/23/00 -0500, Ludwik Kowalski wrote:
>
> Suppose we know nothing about radioactive decay at all. The
> counter counts something. Perhaps these are cars crossing a
> line on a busy highway in consecutive seconds. Who cares
> how many cars are there in the entire country. I can ignore
> all cars beyond a certain limit (the limit depends on how long
> I am counting) and the distribution is exactly the same.

That's right, if you pass to the "certain limit" in a way that captures the
correct physics.

> The experimental distribution gives me the mean number of
> counts; it is = 2.20 per interval.

OK.  That's the quantity that people have been calling pn (the probability
of arrival of a given car, times the number of cars in the country).  The
limit you spoke of is
    n -> large
while
   pn = constant.

which is the limit in which the binomial distribution becomes
indistinguishable from the Poisson distribution.  As you said, n doesn't
directly matter, as long as it is large enough.  It is pn that directly
matters.

> It also gives me the relative
> frequency of 0.24 for recording only one count per interval.
> For my practical purpose the relative frequency is the
> probabiliity p which appear in the binomial distribution.

Nope.  p is very small, because pn is medium-sized and n is huge.