A random variable is a mathematical formalization of a quantity or object that depends on random events. It is a variable whose value is unknown or a function that assigns values to each of an experiments outcomes. Random variables are often used in probability and statistics to quantify outcomes of a random occurrence and can take on many values. They are required to be measurable and are typically real numbers.

There are two types of random variables: discrete and continuous. A discrete random variable is a variable whose possible values are numerical outcomes of a random phenomenon. The probability distribution of a discrete random variable is a list of probabilities associated with each of its possible values. On the other hand, a continuous random variable is not defined at specific values but is defined over an interval of values and is represented by the area under a curve.

A random variable is often denoted by capital Roman letters such as X. The probability that a random variable takes on a value in a measurable set is written as P(X ∈ A) . For example, in an experiment where a person is chosen at random, the persons height can be a random variable. Mathematically, the random variable is interpreted as a function that maps the person to his or her height.

Random variables are often used in econometric or regression analysis to determine statistical relationships among one another. They can be used to calculate probabilities of certain outcomes and to calculate expected values for different types of random variables.