Some probability distributions connected with recording apparatus. II

Abstract

In a previous paper(1) a number of problems in probability were considered arising out of the finite resolving time of a recording apparatus. It was shown that, although the probability distributions themselves are complicated, their Laplace transforms are relatively simple. Recently Feather(2) has discussed a number of additional problems arising in this connexion, including the number of coincidences, and the number of k-clusters. The method developed in (1) is readily applicable to these problems, and it will be shown how complete probability distributions can be derived. An alternative type of recorder is sometimes considered (3) which remains dead as long as events succeed each other at intervals less than τ. The mathematical problem here is somewhat different, but it can again be effectively dealt with by the use of Laplace transforms.