By Kardi Teknomo, PhD .

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I write again equation (5) for your convenient:

Proof Data Revival (5)

We can rearrange equation (5) to give Proof Data Revival :

Proof Data Revival , or

Proof Data Revival (a)

Preparing for other terms:

Proof Data Revival

Proof Data Revival (b)

Proof Data Revival

Proof Data Revival (c)

I write again equation (4) in here:

Proof Data Revival (4)

Putting equation (b) and (c) into equation (4) gives

Proof Data Revival (d)

We want to get the value of Proof Data Revival from equation (d). For this purpose we arrange equation (d) so that it will give a quadratic equation in Proof Data Revival .

Proof Data Revival

Proof Data Revival

Proof Data Revival

Rearrange for Proof Data Revival :

Proof Data Revival

Proof Data Revival (e)

The discriminant of the quadratic equation is

Proof Data Revival

Proof Data Revival (proved)


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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