Chapter 5 Models for discrete random variables

From a mathematical viewpoint any sequence of numbers, $p(r)$, satisfying

$p(r)\ge 0$ for all $r$ and ${\sum }_{r=0}^{\mathrm{\infty }}p(r)=1$,

is a valid pmf corresponding to some random variable. However, we are interested mainly in those random variables which arise from experiments of practical relevance, and thus form plausible models for future statistical modelling. In this chapter we examine some examples of random variables that result from experiments with well-defined physical mechanisms.