Components of Variance
The law of total variance says
where, for example, is understood to mean that the value x at which the conditional variance would be evaluated is allowed to be a random variable, X. In this "law", the inner expectation or variance is taken with respect to Y conditional on X, while the outer expectation or variance is taken with respect to X. This expression represents the overall variance of Y as the sum of two components, involving a prediction of Y based on X. Specifically, let the predictor be the least-mean-squares prediction based on X, which is the conditional expectation of Y given X. Then the two components are:
-
- 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.
| This probability-related article is a stub. You can help Wikipedia by expanding it. |
Read more about this topic: Conditional Variance
Famous quotes containing the words components of, components and/or variance:
“Hence, a generative grammar must be a system of rules that can iterate to generate an indefinitely large number of structures. This system of rules can be analyzed into the three major components of a generative grammar: the syntactic, phonological, and semantic components.”
—Noam Chomsky (b. 1928)
“Hence, a generative grammar must be a system of rules that can iterate to generate an indefinitely large number of structures. This system of rules can be analyzed into the three major components of a generative grammar: the syntactic, phonological, and semantic components.”
—Noam Chomsky (b. 1928)
“There is an untroubled harmony in everything, a full consonance in nature; only in our illusory freedom do we feel at variance with it.”
—Fyodor Tyutchev (1803–1873)