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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.
The experiment contradicts such expectations.
It is tricky experiment to setup.