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).