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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.
In probability theory, the joint probability distribution is the probability distribution of all possible pairs of outputs of two random variables that are defined on the same probability space. The joint distribution can just as well be considered for any given number of random variables.
In the discrete case, it is sufficient to specify a probability mass function assigning a probability to each possible outcome (e.g. when throwing a fair die, each of the six digits “1” to “6”, corresponding to the number of dots on the die, has the probability ).
An alternative parameterization of the distribution gives the probability mass function (=) = () where = and =. [ 1 ] : 208–209 An example of a geometric distribution arises from rolling a six-sided die until a "1" appears.
In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution wherein each of some finite whole number n of outcome values are equally likely to be observed. Thus every one of the n outcome values has equal probability 1/n. Intuitively, a discrete uniform distribution is "a known, finite number ...
1.1 Probability Mass Function. 1.2 Cumulative distribution function. 2 Properties. ... poibin - Python implementation - can compute the PMF and CDF, ...
The probability mass function can be expressed using the gamma function as: (, ...