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Normal Self-Product Distribution

  1. Jan 8, 2009 #1
    Hi all,

    I am trying to evaluate the distribution of a normal distribution producted with itself. On http://mathworld.wolfram.com/NormalProductDistribution.html there is a page about the product distribution in the case of two normals distributions of different standard deviations but the same mean of zero.

    I was hoping someone had derived the normal self-product distribution in the case of a mean not equal to zero and a standard deviation not equal to zero. Does anyone know how to do this or where I should look?


  2. jcsd
  3. Jan 8, 2009 #2


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    Any normally distributed random variable can be expressed in terms of a standard normal random variable; does that help?
  4. Jan 8, 2009 #3
    It might do... do you have an equation of how to express a general normal distribution in terms of the standard normal distribution?
  5. Jan 8, 2009 #4


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    If P is a distribution with mean [itex]\mu[/itex] and standard deviation [itex]\sigma[/itex], then [itex]z= (x- \mu)/\sigma[/itex] has the standard normal distribution.
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