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Adding local short description: "Probability theory and statistics concept", overriding Wikidata description "probability distribution restricted to a subspace of the sample space, normalize to a total probability of one" |
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{{Short description|Probability theory and statistics concept}}
{{refimprove|date=April 2013}}
In [[probability theory]] and [[statistics]], given two [[joint probability distribution|jointly distributed]] [[random variable]]s <math>X</math> and <math>Y</math>, the '''conditional probability distribution''' of <math>Y</math> given <math>X</math> is the [[probability distribution]] of <math>Y</math> when <math>X</math> is known to be a particular value; in some cases the conditional probabilities may be expressed as functions containing the unspecified value <math>x</math> of <math>X</math> as a parameter. When both <math>X</math> and <math>Y</math> are [[categorical variable]]s, a [[conditional probability table]] is typically used to represent the conditional probability. The conditional distribution contrasts with the [[marginal distribution]] of a random variable, which is its distribution without reference to the value of the other variable.
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