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I am looking for multivariate case of a distribution of a product of two normally distributed variables X and Y. The variables are independent. Something similar to this:

http://mathworld.wolfram.com/NormalProductDistribution.html

Except:

  1. Both X and Y are vectors and Gaussians are multivariate $N(\mu_x,\Sigma_x)$ and $N(\mu_y,\Sigma_y)$
  2. Both distributions have non-zero respective means $\mu_x$ and $\mu_y$
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  • $\begingroup$ How are you defining the product of the vectors $X$ and $Y$? Inner product? Term-by-term product? $\endgroup$ – Dilip Sarwate May 14 '13 at 2:45
  • $\begingroup$ term-by-term product $\endgroup$ – krokodil May 14 '13 at 15:12

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