Difference between revisions of "Impossible event"
From Encyclopedia of Mathematics
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| − | An event that, under the given conditions, cannot possibly occur. If | + | <!-- |
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| + | An event that, under the given conditions, cannot possibly occur. If $ ( \Omega , {\mathcal A} , {\mathsf P} ) $ | ||
| + | is a probability space, the impossible event is $ \emptyset \in {\mathcal A} $ | ||
| + | that does not contain any of the elementary outcomes $ \omega \in \Omega $( | ||
| + | the empty set). The impossible event is the complement of the [[Certain event|certain event]] $ \Omega $ | ||
| + | in this probability model, and for this reason it is assigned probability zero: $ {\mathsf P} ( \emptyset ) = 0 $. | ||
Latest revision as of 22:11, 5 June 2020
An event that, under the given conditions, cannot possibly occur. If $ ( \Omega , {\mathcal A} , {\mathsf P} ) $
is a probability space, the impossible event is $ \emptyset \in {\mathcal A} $
that does not contain any of the elementary outcomes $ \omega \in \Omega $(
the empty set). The impossible event is the complement of the certain event $ \Omega $
in this probability model, and for this reason it is assigned probability zero: $ {\mathsf P} ( \emptyset ) = 0 $.
How to Cite This Entry:
Impossible event. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Impossible_event&oldid=15496
Impossible event. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Impossible_event&oldid=15496
This article was adapted from an original article by A.V. Prokhorov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article