By Kardi Teknomo, PhD .
I write again equation (5) for your convenient:
We can rearrange equation (5) to give :
Preparing for other terms:
I write again equation (4) in here:
Putting equation (b) and (c) into equation (4) gives
We want to get the value of from equation (d). For this purpose we arrange equation (d) so that it will give a quadratic equation in .
Rearrange for :
The discriminant of the quadratic equation is
Preferable reference for this tutorial is
Teknomo, Kardi. (2006) Recursive Average and Variance.