Definition
The conditional variance of a random variable Y given that the value of a random variable X takes the value x is
where E is 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 :
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.
Read more about this topic: Conditional Variance
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