# Probability density function

 related topics {math, number, function} {household, population, female} {rate, high, increase} {math, energy, light}

In probability theory, a probability density function (pdf), or density of a continuous random variable is a function that describes the relative likelihood for this random variable to occur at a given point. The probability for the random variable to fall within a particular region is given by the integral of this variable’s density over the region. The probability density function is nonnegative everywhere, and its integral over the entire space is equal to one.

The terms   probability distribution function[1] and   probability function[2] have also sometimes been used to denote the probability density function. However, special care should be taken around this usage since it is not standard among probabilists and statisticians. In other sources,   probability distribution function” may be used when the probability distribution is defined as a function over general sets of values, or it may refer to the cumulative distribution function, or it may be a probability mass function rather than the density. Further confusion of terminology exists because density function has also been used for what is here called the   probability mass function”.[3]