I need a help to solve the question regarding normal distribution. The question is :

If X and Y are standard normal distribution and are independent then how to find the pdf and mgf of XY?

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- Nov 13th 2012, 07:21 AMsumanthapaSuman Thapa
I need a help to solve the question regarding normal distribution. The question is :

If X and Y are standard normal distribution and are independent then how to find the pdf and mgf of XY? - Nov 13th 2012, 08:17 AMabenderRe: Suman Thapa
The (univariate) normal PDF is given by .

When is standard normal, , so that the standard normal PDF is .

is also a standard normal random variable, so its PDF is similarly .

Now, If and are INDEPENDENT, then .

So, . - Nov 13th 2012, 08:42 AMsumanthapaRe: Suman Thapa
Thanks for the solution. But I mean, if Z = XY (product of X and Y), where X and Y are standard normal distribution, then how to find the pdf and moment generating function(mgf) of Z? Could you please help me? Thanks.