## Distribution

The distribution of a variable is a description of the relative numbers of times each possible outcome will occur in a number of trials. The function describing the distribution is called the Probability Function, and the function describing the probability that a given value or any value smaller than it will occur is called the Distribution Function.

Formally, a distribution can be defined as a normalized Measure, and the distribution of a Random Variable is the Measure on defined by setting

where is a Probability Space, is a Measurable Space, and a Measure on with .

See also Continuous Distribution, Discrete Distribution, Distribution Function, Measurable Space, Measure, Probability, Probability Density Function, Random Variable, Statistics

References

Doob, J. L. The Development of Rigor in Mathematical Probability (1900-1950).'' Amer. Math. Monthly 103, 586-595, 1996.