Principle
1) The aim of this experiment is to show that the number of
pulses counted during identical time intervals by a counter tube
which bears a fixed distance to along-lived radiation emitter
correspond to a Poisson´s distribution. A special characteristic of
the Poisson´s distribution can be observed in the case of a small
number of counts n < 20: The distribution is unsymmetrical, i.
e. the maximum can be found among smaller numbers of pulses than
the mean value. In order to show this unsymmetry the experiment is
carried out with a short counting period and a sufficiently large
gap between the emitter and the counter tube so that the average
number of pulses counted becomes sufficiently small.
2) Not only the Poisson's distribution, but also the Guassian
distribution which is always symmetrical is very suitable to
approximate the pulse distribution measured by means of a
long-lived radiation emitter and a counter tube arranged with a
constant gap between each other.A premise for this is a
sufficiently high number of pulses and a large sampling size. The
purpose of the following experiment is to confirm these facts and
to show that the statistical pulse distribution can even be
approximated by a Guassian distribution, when (due to the dead time
of the counter tube) counting errors occur leading to a
distribution which deviates from the Poisson's distribution.
3) If the dead time of the counter tube is no longer small with
regard to the average time interval between the counter tube
pulses, the fluctuation of the pulses is smaller than in the case
of a Poisson's distribution. In order to demonstrate these facts
the limiting value of the mean value (expected value) is compared
to the limiting value of the variance by means of a sufficiently
large sampling size.
What you can learn about
- Poisson's distribution
- Gaussian distribution
- Standard deviation
- Expected value of pulse rate
- Different symmetries of distributions
- Dead time
- Recovering time and resolution time of a counter tube