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Is 2 times normal distribution still a normal distribution please?

  1. Jul 6, 2011 #1
    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. jcsd
  3. Jul 6, 2011 #2
    It is not a normalized PDF, since the total probability sums up to more than 1.
     
  4. Jul 6, 2011 #3
    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?
     
  5. Jul 6, 2011 #4
    Yup, for any A,B > 0, A exp(-x^2/B), normalized, is a normal distribution.
     
  6. Jul 11, 2011 #5
    Oh, thank you very much! pmsrw3
     
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