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I'm trying to understand the origin of the formulas for the $\mu$ and the $\sigma^2$ from this side (stanford):

https://ccrma.stanford.edu/~jos/sasp/Product_Two_Gaussian_PDFs.html

As I have understood actually the product of two Gaussian PDF's is not again a Gaussian PDF. But with the formula from the stanford website I again get a Gaussian PDF.

Where I need help is:

  1. Understand the origin of the two formulas $(\mu, \sigma^2)$
  2. Is the center of the product of two PDF's and the center of a PDF calculated via the two formulas in the same place?

1 Answers 1