By Kardi Teknomo, PhD .
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become
(b)
Question: How can it be?
Proof that
Equivalent to
(change position of term)
Equivalent to
(because )
Equivalent to
(expanding the term of lhs)
Equivalent to
(cancel out )
Equivalent to
(because )
Equivalent to
(because )
Since
and then
Then it is equivalent to
or
Remove t1 term and put rhs to the left become
or
or
See Also:
proof of recursive variance formula
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These tutorial is copyrighted .
Preferable reference for this tutorial is
Teknomo, Kardi. (2006) Recursive Average and Variance.
http://people.revoledu.com/kardi/tutorial/RecursiveStatistic/index.html