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Re: counts in an interval



At 10:23 AM 7/9/00 -0400, Ludwik Kowalski wrote in part:

The average waiting
time (between counting two consecutive Geiger pulses)
was found to be 0.325 seconds, as described yesterday
morning. This makes r=1/0.325=3.08 cnts/s.


The [Poisson] formula (with r*t=3.08*0.2=0.615) makes
the following predictions:

m=0 --> 1445 outcomes (instead of experimental 123)
m=1 --> 890 outcomes (instead of experimental 467)
m=2 --> 274 outcomes (instead of experimental 674)
m=3 --> 56 outcomes (instead of experimental 604)
m=4 --> 7 outcomes (instead of experimental 503)
m=5 --> 1 outcome (instead of experimental 172)
m=6 --> 0 outcome (instead of experimental 85)

One could quibble with some of the predicted numbers, but they're all close
enough for present purposes. The predictions are so grossly ill-fitting
that details don't matter.

The formula would roughly match experimental outcomes
if r*t=15 were used, instead of 0.616. I am puzzled;
something is not right somewhere.

No, that's not right. In fact, the experimental data is a rather good
match to a Poisson distribution with something like rt = 2.77 counts per bin.
If t = 0.2 seconds, that corresponds to r = 13.85 counts per second.

================

Suggestion: Hook the Geiger counter to a speaker and just listen. It will
take only a couple of seconds to determine which of the following numbers
has a chance of being correct.
rt=15 75 counts per second (allegedly derived from histogram)
rt=2.77 13.85 counts per second (jsd fit to histogram)
rt=.616 3.08 counts per second (allegedly derived from interpulse)

Note: each bin is 0.2 seconds, so there are 5 bins per second.

Observation: If we "round off" 2.77 to 3, then the middle rt value is 5
times bigger than the small one, and 5 times smaller than the big
one. This leads to a hypothesis, namely repeated mistakes in converting
between "counts per bin" and "counts per second". However, my crystal ball
is a bit murky at the moment, so other possible explanations can't be ruled
out.