Normal Product Distribution

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.