# Poisson formula

Radioactive decay is a random process, of course. If we observe decays over an interval of time that is very short compared with the lifetime, the number of atoms stays constant to a good approximation. The number of decays over that period of time, on average, should be

 (6)

where we are approximating . In practice, because of fluctuations, there may be more or fewer decays. The probability of observing decays is given by the Poisson distribution:
 (7)

where is the factorial . If we make measurements of the decay over a total time period , then the number of intervals in which exactly decays occur is given by
 (8)

Because of statistical fluctuations, this statement is true only on average.