# Probability density function

From AMS Glossary

## probability density function

(

*Or*density function;*also called*frequency function.) The statistical function that shows how the density of possible observations in a population is distributed.It is the derivative

*f*(*x*) of the distribution function*F*(*x*) of a random variable, if*F*(*x*) is differentiable. Geometrically,*f*(*x*) is the ordinate of a curve such that*f*(*x*)*dx*yields the probability that the random variable will assume some value within the range*dx*of*x*. The density function is nonnegative, and its total integral is unity. Sometimes the probability density function is called the distribution function, but this practice causes confusion and is not recommended.