$X_1 \sim N(\mu_1,\sigma^{2}_1)$
$X_2 \sim N(\mu_2,\sigma^{2}_2)$
What random variable as function of $X_1$ and $X_2$ has p.d.f. which is equal to product of two Gaussians?
Asked
Active
Viewed 32 times
0
-
If the means are $0$, the distribution of a product of two Gaussians is called product normal. You are interested in a more general situation. There is a literature. Searching under product normal should reach some of it. – André Nicolas Jan 29 '16 at 17:27
-
I am not sure what the OP means. – wolfies Jan 29 '16 at 17:31
-
I tried to search in google I received something like this http://mathworld.wolfram.com/NormalProductDistribution.html . But it is p.d.f. of X1*X2 with zero mean....And I' m interesting not in distribution of multiplication of two r.v., but in expression for r.v., s.t. it's p.d.f. is expressed as multiplication – Konstantin Burlachenko Jan 29 '16 at 17:35
-
@wolfies: Nor am I. Clarification would be useful. – André Nicolas Jan 29 '16 at 17:37