Encyclopedia of Systems Biology

2013 Edition
| Editors: Werner Dubitzky, Olaf Wolkenhauer, Kwang-Hyun Cho, Hiroki Yokota

Probability Distributions

  • Winston HaynesEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-9863-7_1178



A probability distribution is a representation of random variables and the associated probabilities of different outcomes. A probability distribution is characterized by a probability density function or probability mass function for continuous or discrete variables, respectively.


Probability Density Function

A probability density function (PDF) is a function which defines the probability of a specific random variable occurring within a statistical distribution for a continuous variable. Given a data observation, the PDF can be utilized to determine the probability of that observation occurring as a random variable.

The integrable function f( x) is a PDF over the space S if it satisfies the following conditions:
  1. (a)

    \( {f(x)> {0,}\quad x \in S} \)

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  1. Hogg RV, Tanis EA (2006) Probability and statistical inference. Pearson Prentice Hall, Upper Saddle River, NJGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  1. 1.Seattle Children’s Research InstituteSeattleUSA