Statistics for Maintenance Modelling: Basic Probability Concepts

# Random Variables and Probability Distributions¤

Although the concept of a random event is a useful one in describing random processes, a more useful concept is that of the random variable, and this leads us to the second approach to modelling uncertainty using probability distributions.

As we've seen, the outcome of an experiment need not be a number. For example, the outcome when a coin is tossed can be 'heads' or 'tails'. However, we often want to represent outcomes as numbers.

A random variable is a function that associates a unique numerical value with every outcome of an experiment. The value of the random variable will vary from trial to trial as the experiment is repeated. There are two types of random variable - discrete and continuous.

## Discrete Random Variables

A discrete random variable is one which may take on only a countable number of distinct values such as 0, 1, 2, 3, 4, ... Discrete random variables are usually (but not necessarily) counts. If a random variable can take only a finite number of distinct values, then it must be discrete. Examples of discrete random variables include:

- the number of children in a family
- the Friday night attendance at a cinema
- the number of patients in a doctor's surgery
- the number of defective light bulbs in a box of ten.