Random values
Performing a simulation of a probability model is based on generation of random values from the probability distributions in the model.
A computer program should normally be used to generate random values. The program Excel contains functions that can be used.
In the rest of this section, we investigate how to generate categorical and numerical values from arbitrary distributions without relying on computer software.
The basis of random number generation is a random value between 0 and 1 for which each possible value is equally likely. Such a value is said to come from a rectangular (or uniform) distribution between 0 and 1 and has the probability density function shown below.
A value can be generated from a rectangular distribution by successively generating random digits (e.g. by rolling a 10-sided die).
The diagram below illustrates generation of a rectangularly distributed value.