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Conditional variance : ウィキペディア英語版
Conditional variance
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==
The conditional variance of a random variable ''Y'' given that the value of a random variable ''X'' takes the value ''x'' is
:\operatorname(Y|X=x) = \operatorname((Y - \operatorname(Y\mid X=x))^\mid X=x),
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 :\operatorname_(Y|x).
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.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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