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).
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.
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.