STANDARD DEVIATION OF DEAD TIME CORRECTION IN COUNTERS
L. Lorne Campbell · Canadian Journal of Physics · 1956
Because of the finite recovery time of counters a correction must be applied to the number of registrations which the counter makes so that a better approximation to the true rate at which events occur may be obtained. It is shown here that, for random events, the standard deviation of the corrected rate is approximately [Formula: see text], where v is the mean rate at which events occur, T is the recovery time of the counter, and t is the duration of the observation. This value of the standard deviation is an asymptotic value which holds for large values of t. As an intermediate result, an asymptotic expression is obtained for the value of the mth moment of the number of registrations in time t. The method used here could also be applied to determine asymptotic expressions for the expected values of other functions of the number of registrations.