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{{Short description|Probability theory and statistics concept}}
{{more citations needed|date=April 2013}}
In [[probability theory]] and [[statistics]], the conditional probability distribution is a probability distribution that describes the probability of an outcome given the occurrence of a particular event. 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.
If the conditional distribution of <math>Y</math> given <math>X</math> is a [[continuous distribution]], then its [[probability density function]] is known as the '''conditional density function'''.<ref>{{cite book |first=Sheldon M. |last=Ross |authorlink=Sheldon M. Ross |title=Introduction to Probability Models |___location=San Diego |publisher=Academic Press |edition=Fifth |year=1993 |isbn=0-12-598455-3 |pages=88–91 }}</ref> The properties of a conditional distribution, such as the [[Moment (mathematics)|moments]], are often referred to by corresponding names such as the [[conditional mean]] and [[conditional variance]].
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