Statistics for Maintenance Modelling: Basic Probability Concepts

# Continuous Random Variables and the Probability Density Function¤

A continuous random variable is one which takes an infinite number of possible values. Continuous random variables are usually measurements. Examples include height, weight, the amount of sugar in an orange and the time required to run a mile.

The way in which probabilities are assigned to discrete random variables is not applicable for continuous random variables, and instead of using a probability mass function, we use a probability density function. Mathematically the probability density function, f(x) is given by the equation:

Unlike the discrete case, f(x) does not give the probability of X = x. General properties of probability density functions are:

- f(x) 0 for - < x <

These two properties come from the fact that:

1. the random variable must take on a value from - to
2. probabilities cannot be negative.