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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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