Probability distribution

In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment.^[1]^[2] It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space).^[3]

For instance, if $X$ is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of $X$ would take the value 0.5 (1 in 2 or 1/2) for $X = heads$ , and 0.5 for $X = tails$ (assuming that the coin is fair). More commonly, probability distributions are used to compare the relative occurrence of many different random values.

Probability distributions can be defined in different ways and for discrete or for continuous variables. Distributions with special properties or for especially important applications are given specific names.

^ Everitt, Brian (2006). The Cambridge dictionary of statistics (3rd ed.). Cambridge, UK: Cambridge University Press. ISBN 978-0-511-24688-3. OCLC 161828328.
^ Ash, Robert B. (2008). Basic probability theory (Dover ed.). Mineola, N.Y.: Dover Publications. pp. 66–69. ISBN 978-0-486-46628-6. OCLC 190785258.
^ Evans, Michael; Rosenthal, Jeffrey S. (2010). Probability and statistics: the science of uncertainty (2nd ed.). New York: W.H. Freeman and Co. p. 38. ISBN 978-1-4292-2462-8. OCLC 473463742.

[:02-1] Everitt, Brian (2006). The Cambridge dictionary of statistics (3rd ed.). Cambridge, UK: Cambridge University Press. ISBN 978-0-511-24688-3. OCLC 161828328.

[2] Ash, Robert B. (2008). Basic probability theory (Dover ed.). Mineola, N.Y.: Dover Publications. pp. 66–69. ISBN 978-0-486-46628-6. OCLC 190785258.

[:1-3] Evans, Michael; Rosenthal, Jeffrey S. (2010). Probability and statistics: the science of uncertainty (2nd ed.). New York: W.H. Freeman and Co. p. 38. ISBN 978-1-4292-2462-8. OCLC 473463742.

[1]

[2]

[3]