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Yes indeed.
(1) Concerning whether the Geiger counter distribution is binomial or
Poisson.
It is both. The Poisson distribution is simply an approximation to the
binomial distribution.
Indeed the PD is a limiting case of the BD.
The Poisson distribution, as I showed in an earlier posting, can
If the Poisson distribution is just an approximation to the binomial
distribution, why bother with the Poisson distribution... why not just use
the binomial distribution?
This misses the point. See above.(1a) Because the binomial distribution cannot be evaluated exactly for
situations involving large n because the binomial distribution requires the
evaluation of n!.
Actually there's a better reason: for large N (the total number of atoms)
and small p (probability of decay per atom, over relevant timescales), then
only the product of pN matters, so eliminating p and N in favor of pN
actually captures a valuable concept.
(1b) Sometimes, approximation methods lead to some insight that might be
more difficult to notice if the approximation were not performed.
Right.
(2) What insights might be included in (1b)?
See my comment under (1a).