A **random variable** is a variable whose value depends on chance, accordingly its value is associated with a probability. A **discrete random variable** is a random variable whose possible values can be listed. A **probability distribution** is a listing of the possible values and corresponding probabilities of a discrete random variable, often represented by a formula.

A graph of the probability distribution that displays the probability of each value, represented by a vertical bar whose height equals the probability and possible values of a discrete random variable on the horizontal axis is called **probability histogram** or **proportion histogram**.

The **sum of the probabilities of a discrete random variable** for any discrete random variable \(X\) is written as

\[\sum_{i=1}^{N}P(X = x_i) = 1\]

In a large number of independent observations of a random variable \(X\) the probability histogram will approximate the probability distribution for \(X\) (Weiss 2010).