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Elementary event





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Inprobability theory, an elementary event, also called an atomic eventorsample point, 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 corresponding to precisely one outcome.

The following are examples of elementary events:

Probability of an elementary event

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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.

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 atomsoratomic 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-algebraon  and not necessarily the full power set.

See also

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References

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

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    Last edited on 13 March 2024, at 03:23  





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    This page was last edited on 13 March 2024, at 03:23 (UTC).

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