Is 2 times normal distribution still a normal distribution please?

1. Jul 6, 2011

wall_e

Hi, it will be a very silly question, excuse me plz.

I am wondering whether

3/(sqrt(2pi delta^2)) exp(-x^2/(2delta^2)) is still a normal distribution please?

where mean is 0, delta^2 is the variance.

Thank you very very much.

Also, how to understand this related to the kurtois please? Many many thanks again.

2. Jul 6, 2011

pmsrw3

It is not a normalized PDF, since the total probability sums up to more than 1.

3. Jul 6, 2011

wall_e

thank you very much, pmsrw3.

So if I want to choose a form A exp(-x^2/B) to fit a pdf, where A and B are parameters, after normalization, I will get a normal distribution?

4. Jul 6, 2011

pmsrw3

Yup, for any A,B > 0, A exp(-x^2/B), normalized, is a normal distribution.

5. Jul 11, 2011

wall_e

Oh, thank you very much! pmsrw3