Discrete Distributions

Abstract

A discrete random variable is a random variable taking only values on integers. The distribution of a discrete random variable X is determined by its probability mass function, p _k = Prob(X = k). It is also called probability vector if its support is bounded from below. In the latter case we assume without loss of generality that X is only taking values on the nonnegative integers. We then write (p ₀ ,p ₁ , …) for the probability vector. Analogously to the continuous case we use the terms quasi-probability mass function for a nonnegative summable function that need not be normalized.