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 .

**References**

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

© 1996-9

1999-05-24