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

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

**Citation**

The E-Learning project SOGA-Py was developed at the Department of Earth Sciences by Annette Rudolph, Joachim Krois and Kai Hartmann. You can reach us via mail by soga[at]zedat.fu-berlin.de.

You may use this project freely under the Creative Commons Attribution-ShareAlike 4.0 International License.

Please cite as follow: *Rudolph, A., Krois, J., Hartmann, K. (2023): Statistics and Geodata Analysis
using Python (SOGA-Py). Department of Earth Sciences, Freie Universitaet Berlin.*