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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
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 pmf allows the computation of probabilities of events such as (>) = / + / + / = /, and all other probabilities in the distribution. Figure 4: The probability mass function of a discrete probability distribution. The probabilities of the singletons {1}, {3}, and {7} are respectively 0.2, 0.5, 0.3. A set not containing any of these points has ...
It is equivalent to, and sometimes called, the z-transform of the probability mass function. Other generating functions of random variables include the moment-generating function , the characteristic function and the cumulant generating function .
Its probability mass function depends on its parameterization and support. When supported on , the probability mass function is (=) = where =,,, … is the number of trials and is the probability of success in each trial.
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 and statistics, the logarithmic distribution (also known as the logarithmic series distribution or the log-series distribution) is a discrete probability distribution derived from the Maclaurin series expansion = + + +.