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If I roll a pair of dice and observe five dots, then x_i=5 with no
uncertainty. That works with dice, but how about the measurement of
the period of a pendulum?
Is there a _simple_ measure that you'd suggest for characterizing the
overlap of the distributions? I can get them as far as conceptually
'getting' that distributions that don't overlap aren't likely the
same, and those with significant overlap are, but I haven't yet found
a _simple_ measure that will allow them to compare (at least, not one
that I'm super happy with: I've had them look for overlap within 1
sigma of the mean, which was easy to do, but not necessarily on good
footing. ...or maybe it is? C onceptually, I'm OK with it, but I'd
like a comparison measure without doing T tests or similar).
There's uncertainty in the measurement, as well as uncertainty in the
distribution of the expected value of the measurement