By S. Penczek

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It is left as an exercise for the reader to show that under the conditions mentioned above, the binomial distribution takes the form known as the Poisson distribution, Pn = mn − m e n! 50) Errors of Radiation Counting 31 where Pn is the probability of observing the outcome n when the average for a large number of trials is m. The Poisson distribution has wide applications in many diverse fields, such as decay of nuclei, persons killed by lightning, number of telephone calls received in a switchboard, emission of photons by excited nuclei, appearance of cosmic rays, and so on.

6. Imperfect method of measurement in most cases. 7. Unknown exact initial state of the system. Or, even if the initial state is known, it is impossible to follow the evolution of the system. For example, to determine the state of a gas in a container, one should know the exact position and velocity of every molecule at t = 0. Even if this is known, how practical is it to follow 1020 atoms or molecules moving in a box? 8. Statistical nature of some processes, for example, radioactive decay. There is a probability that an atom of a radioactive isotope will decay in the next 10 s, and this is as much information as one can report on this matter.

The determination of this error is an integral part of any radiation measurement. 3 ERRORS AND ACCURACY AND PRECISION OF MEASUREMENTS A measurement is an attempt to determine the value of a certain parameter or quantity. Anyone attempting a measurement should keep in mind the following two axioms regarding the result of the measurement: Axiom 1: No measurement yields a result without an error. Axiom 2: The result of a measurement is almost worthless unless the error associated with that result is also reported.