I'm trying to understand the contents of this web-page which suggest that multiplying two Gaussian functions together produce a new Gaussian function with a new mean and variance.
Say I have the two following Gaussian functions:
The web-page state that the new mean and variance to be:
I start by multiplying the two functions, but I am unable to get the result into Gaussian form such that I can extract the new mean and variance. Any tips on how these values were calculated?