joint theorem | multivariate 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_1 X_2 X_3 X_4〉 = 〈X_1 X_2〉〈X_3 X_4〉 + 〈X_1 X_3〉〈X_2 X_4〉 + 〈X_1 X_4〉〈X_2 X_3〉, etc. Given an odd number of variates, 〈X_1 〉 | = | 0 〈X_1 X_2 X_3〉 | = | 0, etc.