We obtain a strong law of large numbers and a functional central limit theorem, as t , for the number of records up to time t and the Lebesgue measure (length) of the subset of the time interval [0,t] during which the Poisson process is in a record lifetime.

Computer-based tests with randomly generated questions allow a large number of different tests to be generated. Given a fixed number of alternatives for each question, the number of tests that need to be generated before all possible questions have appeared is surprisingly low.

The convolution of regularly varying probability densities is proved asymptotic to their sum, and hence is also regularly varying. Extensions to rapid variation, O-regular variation, and other types of asymptotic decay are also given.

The moment index of a nonnegative random variable X has the property that the moment index of the minimum of two independent r.v.s X and Y is greater than or equal to the sum of the moment indices of X and Y. We characterize conditions under which equality holds for a given r.v. X and every independent nonnegative r.v. Y, and discuss extensions to related r.v.s and their distributions.