Invariance of a random discrete distribution under size-biased permutation is equivalent to a conjunction of symmetry conditions on its finite-dimensional distributions. This is applied to ...

Discrete variable's values are also "disjoint," so we have the gaps in a discrete variable's probability distribution graph. While the formula for the expected value of a discrete variable may seem ...

In this paper we introduce discrete-time semi-Markov random evolutions (DTSMREs) and study asymptotic properties, namely, averaging, diffusion approximation, and diffusion approximation with ...

It includes discrete and continuous random variables, their probability distributions and analytical and statistical methods for determining the mean, variance and higher order moments that ...