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Probability mass function

The distribution of a discrete random variable can be characterized through its probability mass function (pmf). The probability that a given number will be the realization of a discrete random variable is equal to the value taken by its pmf in correspondence of that number.

Definition

In formal terms, the probability mass function of a discrete random variable X is a function [eq1] such that[eq2]where [eq3] is the probability that the realization of the random variable X is equal to x.

Example

Suppose a random variable X can take only three values (1, 2 and 3), each with equal probability. Its probability mass function is[eq4]

More details

You can find an in-depth discussion of probability mass functions in the lecture entitled Random variables.

Related concepts

Related concepts can be found in the following glossary entries:

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