Normal Self-Product Distribution

[natski]

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?

Cheers,

Natski

 

[Hurkyl]

Any normally distributed random variable can be expressed in terms of a standard normal random variable; does that help?

 

[natski]

It might do... do you have an equation of how to express a general normal distribution in terms of the standard normal distribution?

 

[HallsofIvy]

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