Is 2 times normal distribution still a normal distribution please?

AI Thread Summary
The discussion centers on whether the function 3/(sqrt(2pi delta^2)) exp(-x^2/(2delta^2)) qualifies as a normal distribution, concluding it is not due to its total probability exceeding 1. Participants clarify that normalizing the function A exp(-x^2/B) with positive parameters A and B results in a valid normal distribution. Additionally, the conversation touches on understanding kurtosis in relation to these distributions. The importance of normalization for probability density functions is emphasized throughout the discussion. Overall, normalization is crucial for defining a proper normal distribution.
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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.
 
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It is not a normalized PDF, since the total probability sums up to more than 1.
 
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?
 
Yup, for any A,B > 0, A exp(-x^2/B), normalized, is a normal distribution.
 
Oh, thank you very much! pmsrw3
 

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