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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]
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.
A discrete probability distribution is applicable to the scenarios where the set of possible outcomes is discrete (e.g. a coin toss, a roll of a die) and the probabilities are encoded by a discrete list of the probabilities of the outcomes; in this case the discrete probability distribution is known as probability mass function.
Binomial probability mass function and normal probability density function approximation for n = 6 and p = 0.5. If n is large enough, then the skew of the distribution is not too great. In this case a reasonable approximation to B(n, p) is given by the normal distribution (, ()),
The probability mass function of this distribution, over possible outcomes k, is (;) = {=, = = [3] This can also be expressed as ... The Likelihood Function for a ...
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)
Probability mass function [ edit ] For a natural number m ≥ 1 and real parameters p , r with 0 < p ≤ 1 and – m < r < – m + 1 , the probability mass function of the ExtNegBin( m , r , p ) distribution is given by
The reference [13] discusses techniques of evaluating the probability mass function of the Poisson binomial distribution. The following software implementations are based on it: The following software implementations are based on it:
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