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For any four zero mean Gaussian random variables X1 X2

For any four zero- mean Gaussian random variables X1, X2, X3, and X4, show that .

E [X1X2X3X4] = E [X1X2] E[X3X4] + E [X1X3] E [X2X4] + E [X1X4] E [X2X3]

You might want to use the result of the previous exercise. Note: This useful result is referred to as the Gaussian moment- factoring theorem and allows us to decompose fourth- order moments into a series of simpler second- order moments.

E [X1X2X3X4] = E [X1X2] E[X3X4] + E [X1X3] E [X2X4] + E [X1X4] E [X2X3]

You might want to use the result of the previous exercise. Note: This useful result is referred to as the Gaussian moment- factoring theorem and allows us to decompose fourth- order moments into a series of simpler second- order moments.

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