Random Variable

A random variable, also called a random quantity, aleatory variable or stochastic variable, is a mathematical formalization of a quantity or object that depends on random events; despite its name, the term refers not to randomness or variability itself but to a mathematical function whose domain is the set of possible outcomes in a sample space and whose range is a measurable space, typically a subset of the real numbers. In the formal language of measure theory, a random variable is a measurable function from a probability measure space, called the sample space, to a measurable space, and the resulting pushforward measure is called the distribution of the random variable, a probability measure on the set of its possible values; two random variables can share an identical distribution while still differing in significant ways, such as independence. It is common to distinguish discrete random variables, valued in a countable set, from absolutely continuous random variables, valued in an interval of real numbers, and according to George Mackey, Pafnuty Chebyshev was the first person to think systematically in terms of random variables.