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In probability and statistics, a probability mass function (PMF) is a function that gives the probability that a discrete random variable is exactly equal to some value. 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 probability density function (PDF) in that the latter is associated with continuous rather than discrete random variables; the values of the probability density function are not probabilities as such: a PDF must be integrated over an interval to yield a probability.

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