The probability mass function of a discrete random variable is the function . It assigns the probability of each possible value and satisfies

and

where the sum is over the possible values of .

Unlike a probability density function, a probability mass function gives point probabilities directly, without integration. For several discrete random variables, the joint probability mass function is (Cover and Thomas 2006, pp. 13 and 16).

See also

Discrete Distribution, Joint Distribution, Probability, Probability Chain Rule, Probability Density Function, Random Variable

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References

Cover, T. M. and Thomas, J. A. Elements of Information Theory, 2nd ed. Hoboken, NJ: Wiley, Ch. 2, 2006.

Cite this as:

Weisstein, Eric W. "Probability Mass Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ProbabilityMassFunction.html

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