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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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 .
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.
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