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In [[probability theory]] and [[statistics]], a '''conditional variance''' is the [[variance]] of a [[conditional probability distribution]]. That is, it is the variance of a [[random variable]] given the value(s) of one or more other variables. Particularly in [[econometrics]], the conditional variance is also known as the '''scedastic function''' or '''skedastic function'''. Conditional variances are important parts of [[autoregressive conditional heteroskedasticity]] (ARCH) models.
==Definition==
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:<math>\operatorname{Var}(Y|X=x) = \operatorname{E}((Y - \operatorname{E}(Y\mid X=x))^{2}\mid X=x),</math>
where E is the [[conditional expectation]], i.e. the [[expectation operator]] with respect to the [[conditional distribution]] of ''Y'' given that the ''X'' takes the value ''x''. An alternative notation for this is :<math>\operatorname{Var}_{Y\mid X}(Y|x).</math>
The above may be stated in the alternative form that, based on the [[conditional distribution]] of ''Y'' given that the ''X'' takes the value ''x'', the conditional variance is the [[variance]] of this [[probability distribution]].
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:*the average of the variance of ''Y'' about the prediction based on ''X'', as ''X'' varies;
:*the variance of the prediction based on ''X'', as ''X'' varies.
==Further reading==
* {{cite book |first=George |last=Casella |first2=Roger L. |last2=Berger |title=Statistical Inference |___location= |publisher=Wadsworth |edition=Second |year=2002 |isbn=0-534-24312-6 |pages=151–52 |url=https://books.google.com/books?id=0x_vAAAAMAAJ&pg=PA151 }}
[[Category:Statistical deviation and dispersion]]
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