Importance of the Gaussian Distribution for Radiation Measurements

This result is known as the central limit theorem and holds for any random sample of variables with finite standard deviation. 

In reality, no distribution of experimental data can be exactly Gaussian, since the Gaussian extends from — to + . But for all practical purposes, the approximation is good and it is widely used because it leads to excellent results. 

It is worth reminding the reader that both the binomial (Fig. 2.2) and the Poisson (Fig. 2.3) distributions resemble a Gaussian under certain conditions. This observation is particularly important in radiation measurements. 

The results of radiation measurements are, in most cases, expressed as the number of counts recorded in a scaler. These counts indicate that particles have interacted with a detector and produced a pulse that has been recorded. The particles, in turn, have been produced either by the decay of a radioisotope or as a result of a nuclear reaction. In either case, the emission of the particle is statistical in nature and follows the Poisson distribution. However, as indicated in Sec. 2.9, if the average of the number of counts involved is more than about 20, the Poisson approaches the Gaussian distribution. For this reason, the 

The following very important conclusion is drawn from this result  

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