The above histogram shows the distribution of 
lifetimes observed from many decays.
The number of particles with lifetime t is proportional to
e-t/T, where T is the mean lifetime. Hence, if we have a
linear scale on the y-axis, we should get an exponentially decaying distribution. Alternatively, if
we have a logarithmic scale on the y-axis, we should get a straight line (of gradient -1/T).
Use the scrollbar to adjust the number of events to be included in the histogram. You can also adjust the number of bins (bars on the histogram), and can switch between linear and logarithmic scales on the y-axis.
You should find the following:
- If you include too few events or have too many bins, you do not get a smooth distribution. Statistical fluctuations tend to dominate.
- If the bins are too wide, real detail may end up being obscured if the bin stretches over genuine variations in the distribution.
- Having a logarithmic scale exaggerates the appearance of the fluctuations at the higher end of the distribution (where there are fewer events).
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