Estimating the mean and variance of measurements from serial radioactive decay schemes with emphasis on 222Rn and its short-lived progeny

Classically, the mean and variance of radioactivity measurements are estimated from poisson distributions. However, the random distribution of observed events is not poisson when the half-life is short compared with the interval of observation or when more than one event can be associated with a single initial atom. Procedures were developed to estimate the mean and variance of single measurements of serial radioactive processes. Results revealed that observations from the three consecutive alpha emissions beginning with 222Rn are positively correlated. Since the poisson estimator ignores covariance terms, it underestimates the true variance of the measurement. The reverse is true for mixtures of radon daughters only. (author)