Conditional probability distribution: Difference between revisions

Revision as of 21:40, 17 August 2004

Revision as of 21:41, 17 August 2004

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Given two jointly distributed [[random variable]]s ''X'' and ''Y'', the '''conditional probability distribution''' of ''Y'' given ''X'' (written "''Y'' | ''X''") is the [[probability distribution]] of ''Y'' when ''X'' is known to be a particular value.

For [[discrete random variable]]s, the [[conditional probability]] mass function can be written as ''P''(''Y'' = ''y'' | ''X'' = ''x''). From the definition of [[Bayes'conditional theoremprobability]], this is

:<math>P(Y=y|X=x) = \frac{P(X=x,Y=y)}{P(X=x)}= \frac{P(X=x|Y=y) P(Y=y)}{P(X=x)}</math>