Conditional probability distribution: Difference between revisions

Revision as of 05:34, 10 April 2005

Revision as of 13:12, 23 May 2005

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

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

Similarly for [[continuous random variable]]s, the conditional [[probability density function]] can be written as ''p''_''Y''|''X''(''y'' | ''x'') and this is