# 5Probability Density Function

The probability density function (PDF) is a mathematical function that represents the distribution of a dataset. For example, if we were to throw a pair of unbiased six‐sided dice 36 times, we would expect (on average) the distribution of the total score to be that shown by Figure 5.1. This shows the *frequency distribution*. To convert it to a *probability distribution* we divide each frequency by the total number of throws. For example, a total score of 5 would be expected to occur four times in 36 throws and so has a probability of 4/36 (about 0.111 or 11.1%). Figure 5.2 shows the resulting probability distribution.

Throwing dice generates a *discrete* distribution; in this case the result is restricted to integer values. Probability should not be plotted as continuous line. The probability of a non‐integer result is zero. But we can develop an equation for the line. In this case, if *x* is the total scored, the probability of scoring *x* is

Because *x* is discrete this function is known as the *probability mass function (PMF)*. If the distribution were continuous ...

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