# Probability distribution

From AMS Glossary

## probability distribution

The mathematical description of a random variable in terms of its admissible values and the probability associated, in an appropriate sense, with each value.

The probability distribution of a continuous variate is defined by stating the mathematical equation of the distribution function

*F*(*x*) or the probability density function*f*(*x*) (if it exists) together with the range over which the equation holds. The probability distribution of a discrete variate is commonly defined by stating the equation for the probability*p*(*x*) that the variate will assume any particular value*x*, and indicating what values are possible.