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Re: [Phys-l] Poisson stat.



Statistically, rolling dice is a classic example of a binomial
distribution, not a Poisson distribution.

For a binomial distribution, an event either happens or doesn't happen
once during a trial (for example, a die either does or does not come up
"6" on each role).
For a Poisson distribution, the event occurs randomly in time (or space)
with some average rate, but you can get 2 or more occurrences. (for
example, a radioactive sample has an average of 1/6 decay per second,
but could easily have 2 or 3 occurrences in any particular second).

The good news is that the Poisson distribution is a limiting case of the
binomial distribution, so it can be used to model this process. Here,
the combination of 100 binomial trials can be well-approximated by a
single Poisson trial with an average of 100/6 occurrences per trial.
Although it is not perfect -- for example, the Poisson approximation
for the probability of 17 occurrences of "6" in 100 die roles is 9.60%,
while the true binomial probability is 10.52%. (which you can easily
confirm with Excel).


Tim F