Conclusion
The assumption that the statistics of nuclear decay is governed
by the Poisson statistics is only an approximate representation of
reality. This approximation becomes inaccurate when the decay of
a radioactive sample is considered over the time period which is
comparable with the half-lives of the radioisotope. However, the
above considerations do not directly apply to counting statistics when
considering detection of radioactive events because low efficiency
of the detection makes the assumption of Poisson statistics an almost
perfect approximation