Elementary event

"Basic outcome" and "Atomic event" redirect here. For atomic events in computer science, see linearizability.

In probability theory, an elementary event (also called an atomic event or simple event) is an event which contains only a single outcome in the sample space.[1] Using set theory terminology, an elementary event is a singleton. Elementary events and their corresponding outcomes are often written interchangeably for simplicity, as such an event corresponds to precisely one outcome.

The following are examples of elementary events:

Probability of an elementary event

Elementary events may occur with probabilities that are between zero and one (inclusively). In a discrete probability distribution whose sample space is finite, each elementary event is assigned a particular probability. In contrast, in a continuous distribution, individual elementary events must all have a probability of zero because there are infinitely many of them then non-zero probabilities can only be assigned to non-elementary events.

Some "mixed" distributions contain both stretches of continuous elementary events and some discrete elementary events; the discrete elementary events in such distributions can be called atoms or atomic events and can have non-zero probabilities.[2]

Under the measure-theoretic definition of a probability space, the probability of an elementary event need not even be defined. In particular, the set of events on which probability is defined may be some σ-algebra on S and not necessarily the full power set.

See also


  1. Wackerly, Denniss; William Mendenhall; Richard Scheaffer. Mathematical Statistics with Applications. Duxbury. ISBN 0-534-37741-6.
  2. Kallenberg, Olav (2002). Foundations of Modern Probability (2nd ed.). New York: Springer. p. 9. ISBN 0-387-94957-7.

This article is issued from Wikipedia - version of the 11/17/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.