# Probability Density When dealing with real numbers, we should not be asking the question that our random variable $X$ is *equal* to any particular number. That is because $X$ can take on an infinite set of real numbers for a given interval. Rather, we should be asking what the probability is that $X$ is *close* to a single number. We capture the notion of being close to a number with a *probability density function*. If the probability density around a point $x$ is large, then that means the random variable $X$ is likely to be close to $x$.  --- Date: 20210722 Links to: [Mathematics MOC](Mathematics%20MOC.md) Tags: #review References: * [Good post on what it fully means](https://mathinsight.org/probability_density_function_idea)