Statistical error in counting experiments

Abstract

Experiments in which single particles are studied with the aid of counters would, in principle, lead to an exact determination of the statistical laws governing the behaviour of these particles if the number of counted particles were infinitely large. With a finite number of counts, however, a finite statistical error will always remain. This error depends upon the number of counts and upon the way in which one makes use of the counter readings to calculate the parameters entering into the statistical laws. The purpose of the following investigation is to show for some typical cases which way of calculating has to be adopted in order to make the error a minimum.