The Gaussian joint variable theorem, also called the multivariate theorem, states that given an even number of variates from a normal distribution with means all 0,
 |
(1)
|
etc. Given an odd number of variates,
 |  |  |
(2)
|
 |  |  |
(3)
|
etc.
Gaussian Joint Variable Theorem
Explore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Gaussian Joint Variable Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GaussianJointVariableTheorem.html