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The graph of a probability mass function. All the values of this function must be non-negative and sum up to 1. In probability and statistics, a probability mass function (sometimes called probability function or frequency function [1]) is a function that gives the probability that a discrete random variable is exactly equal to some value. [2]
In statistics, especially in Bayesian statistics, the kernel of a probability density function (pdf) or probability mass function (pmf) is the form of the pdf or pmf in which any factors that are not functions of any of the variables in the domain are omitted. [1] Note that such factors may well be functions of the parameters of the
Besides the probability function, the cumulative distribution function, the probability mass function and the probability density function, the moment generating function and the characteristic function also serve to identify a probability distribution, as they uniquely determine an underlying cumulative distribution function. [10]
The probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of independent random variables is the convolution of their corresponding probability mass functions or probability density functions respectively.
In probability theory and statistics, the Poisson distribution (/ ˈ p w ɑː s ɒ n /; French pronunciation:) is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time if these events occur with a known constant mean rate and independently of the time since the last event. [1]
The joint probability mass function of and defines probabilities for each pair of outcomes. All possible outcomes are (=, =), (=, =), (=, =), (=, =). Since each outcome is equally likely the joint probability mass function becomes
The probability generating function is an example of a generating function of a sequence: see also formal power series. It is equivalent to, and sometimes called, the z-transform of the probability mass function.
The probability mass function of a Poisson-distributed random variable with mean μ is given by (;) =!.for (and zero otherwise). The Skellam probability mass function for the difference of two independent counts = is the convolution of two Poisson distributions: (Skellam, 1946)
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