Random variable

A random variable is a function that assigns a value in a sample space to an element of an arbitrary set (James 1992; Pawlowsky-Glahn et al. 2015). It is a model for a random experiment: the arbitrary set is an abstraction of the experimental conditions, the values taken by the random variable are in the sample space, and the function itself models the assignment of outcomes, thus also describing its frequency of appearance. In simpler terms, for the purpose of this presentation, a random variable is a function that assigns to each of the outcomes of a random experiment a value with a certain probability. A random variable also goes by stochastic variable and aleatory variable. Random variables are usually annotated as Roman capital letters, such as X or Y.