| 词条 | Elementary event |
| 释义 |
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 eventElementary 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
References1. ^{{cite book | last = Wackerly | first = Denniss |author2=William Mendenhall |author3=Richard Scheaffer | title = Mathematical Statistics with Applications | publisher = Duxbury | isbn = 0-534-37741-6}} 2. ^{{cite book | last = Kallenberg | first = Olav | title = Foundations of Modern Probability | edition = 2nd | year = 2002 | page = 9 | url = https://books.google.com/books/about/Foundations_of_Modern_Probability.html?id=L6fhXh13OyMC | publisher = Springer | location = New York | isbn = 0-387-94957-7}}
1 : Experiment (probability theory) |
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