It is shown that in a sequence of random events, the expected distribution of interval-sizes in a run of given duration differs from the Bateman distribution when the counting rate is different from the average one. The formula for "local" size-distribution to be expected for such a run is derived by the use of Bayes' theorem. It is pointed out that this theorem is useful in discussing the properties of any statistical system which is known to be in a condition differing from the idealized equilibrium state.

• Received 9 October 1939

DOI:https://doi.org/10.1103/PhysRev.56.1165