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##

Weighted average

The weighted average can be defined by:

,
where the constants
have the properties that,

and

The expected value of the weighted average is,

and the variance is :

for

since sample *i* is independent of sample *j*. We know that
for all *i*, so :

,

where
is the variance of a single variable.

If
then
.

*Yishay Mansour*

*1999-12-16*