The distribution of a product of two normally distributed variates 
and 
with zero means and variances 
and 
is given by
 |  |  |
(1)
|
 |  |  |
(2)
|
where 
is a delta function and 
is a modified
Bessel function of the second kind. This distribution is plotted above in red.
The analogous expression for a product of three normal variates can be given in terms of Meijer G-functions as
 |
(3)
|
plotted above in blue.
