product of N normal distributions

[Camilo]

We are given N normal functions, with means \mu_i, and variances \sigma_i^2, i in 1...N.

I need to find a formula for the product of the N functions.

The case N=2 is easy to find online:

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

but I have found nothing regarding the general case.

Because N=2 in normal, we know that the general result is normal, with a scaling factor. I need formulas for the scaling factor, the mean, and the variance.

Help is much appreciated!

 

[Dason]

Where exactly does it say that the result is a normal distribution?

 

[Camilo]

Where exactly does it say that the result is a normal distribution?

I'm not really sure why my responses are not getting posted. I've tried twice.
Anyway, you are right that it is not clear from the link. You can find the statement here, under the Properties section:
http://en.wikipedia.org/wiki/Gaussian_function