Is 2 times normal distribution still a normal distribution please?

[wall_e]

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

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.

 

[pmsrw3]

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

 

[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?

 

[pmsrw3]

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

 

[wall_e]

Oh, thank you very much! pmsrw3