ABSTRACT
This chapter aims to specify what is meant by random variables and generally to provide revision of the material to be used. Transforming random variables is a common statistical practice, and one which is often utilized in simulation. A geometric random variable provides the waiting-time measured by the number of trials until the first success. Just as the geometric and negative-binomial distributions describe waiting times when time is measured in integer units, the exponential and gamma distributions describe waiting times when time is a continuous quantity. Mardia considers families of bivariate distributions, while Douglas describes the interesting distributions which can result from special combinations of distributions such as the binomial and Poisson. The simplest continuous random variables have uniform distributions. The exponential and gamma distributions describe only non-negative random variables, but the exponential distribution forms the basis of the Laplace distribution.
