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The questions that were being asked (arrival times and various
cumulative and marginal distributions) are purely mathematical
questions. They contain no physics whatsoever, and there's
no point in pretending otherwise.
For the stated purposes one is no worse off, indeed better off, using excel
rather than the Geiger counter.
But I completely agree that a different experiment -- a real hands-on
experiment -- would have value. That's why I suggested using dice.
Finally, as instructors we need to note that students take on our own biases
very quickly. If we (or a prior instructor) talk up experiment as the
ultimate authority, then students will find experiments striking. If instead
we talk up the mathematics, then elegant presentations may have great
impact.
It's not an all-or-nothing situation.
There are some mathematical questions that require mathematical answers.
There are some experimental questions that require experimental answers.
There are some questions that can be attacked either way.