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,
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(1)
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etc. Given an odd number of variates,
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(2)
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(3)
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etc.
Gaussian Joint Variable Theorem
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Cite this as:
Weisstein, Eric W. "Gaussian Joint Variable Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GaussianJointVariableTheorem.html