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Probability Mass Function (PMF) ○꠹｜Definition｜1st｜20260604203856-00-⌔

Probability mass function - Wikipedia

Probability mass function

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In probability and statistics, a probability mass function (sometimes called probability function or frequency function1) is a function that gives the probability that a discrete random variable is exactly equal to some value.2 Sometimes it is also known as the discrete probability density function. The probability mass function is often the primary means of defining a discrete probability distribution, and such functions exist for either scalar or multivariate random variables whose domain is discrete.

A probability mass function differs from a continuous probability density function (PDF) in that the latter is associated with continuous rather than discrete random variables. A continuous PDF must be integrated over an interval to yield a probability.3

The value of the random variable having the largest probability mass is called the mode.

Printed 2026-06-28.

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Footnotes

  1. 7.2 - Probability Mass Functions | STAT 414 - PennState - Eberly College of Science ↩

  2. Stewart, William J. (2011). Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling. Princeton University Press. p. 105. ISBN 978-1-4008-3281-1. ↩

  3. A modern introduction to probability and statistics: understanding why and how. Dekking, Michel, 1946-. London: Springer. 2005. ISBN 978-1-85233-896-1. OCLC 262680588. ↩

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