### Sample Variance

**Definition: **
The *sample variance* of a set of
samples from a particular
realization of a *stationary stochastic process*
is defined
as *average squared magnitude* after removing the *known mean*:

(C.20) |

The sample variance is a

*unbiased estimator*of the true variance when the

*mean is known*,

*i.e.*,

(C.21) |

This is easy to show by taking the expected value:

When the mean is *unknown*, the sample mean is used in its place:

(C.23) |

The normalization by instead of is necessary to make the sample variance be an

*unbiased*estimator of the true variance. This adjustment is necessary because the sample mean is

*correlated*with the term in the sample variance expression. This is revealed by replacing with in the calculation of (C.22).

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Cross-Correlation

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Variance