The Statistical Error of Radiation Measurements

Radioactive decay is a truly random process that obeys the Poisson distribution, according to which the standard deviation of the true mean m is. However, the true mean is never known and can never be found from a finite number of measurements. But is there a need for a large number of measurements  

Suppose one performs only one measurement and the result is n counts. The best estimate of the true mean, as a result of this single measurement, is this number n. If one takes this to be the mean, its standard deviation will be i/n.  

Indeed, this is what is done in practice. The result of a single count n is reported as n i/iT, which implies that 

Consider now a series of N counting measurements with the individual results n li=i..n- It is assumed that the counts , were obtained under 

The average n is the best estimate of a Poisson distribution of which the outcomes are members. The standard deviation of the Poisson 

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