Bayes’ theorem


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states

Let (An) be a sequence of mutually exclusive eventsMathworldPlanetmath whose union (http://planetmath.org/Union) is the sample space and let E be any event. All of the events have nonzero probability (P(E)>0 and P(An)>0 for all n). Bayes’ Theorem states

P(Aj|E)=P(Aj)P(E|Aj)iP(Ai)P(E|Ai)

for any Aj(An).

A simpler formulation is:

P(A|B)=P(B|A)P(A)P(B)

For two events, A and B (also with nonzero probability).

References

  • 1 Milton, J.S., Arnold, Jesse C., Introduction to Probability and Statistics: Principles and Applications for Engineering and the Computing Sciences, McGraw Hill, 1995.
Title Bayes’ theorem
Canonical name BayesTheorem
Date of creation 2013-03-22 12:02:13
Last modified on 2013-03-22 12:02:13
Owner akrowne (2)
Last modified by akrowne (2)
Numerical id 11
Author akrowne (2)
Entry type Theorem
Classification msc 60-00
Classification msc 62A01
Synonym Bayes’ Rule
Related topic ConditionalProbability