Gaussian Joint Variable Theorem
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,
| <X_1X_2X_3X_4>=<X_1X_2><X_3X_4>+<X_1X_3><X_2X_4>+<X_1X_4><X_2X_3>, |
(1)
|
etc. Given an odd number of variates,
<X_1> =
(2)
<X_1X_2X_3> = 0,
(3)
etc.
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Cite this as:
Weisstein, Eric W. "Gaussian Joint Variable Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GaussianJointVariableTheorem.html