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

Question:

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.