. Wick's theorem (also Isserli's theorem ) 10 points] Prove the following result: Let X be a jointly Gaussian zero-mean 2n-dimensional vector with covariance matrix C. Then E(X1X2 . . . Xan) = EIIE(XX,) EII stands for summing over all distinct ways of partitioning the 2n random variables (possibly perfectly correlated, i.e., X1 = Xx for some l # k) into n pairs of (Xi, X;), and each summand is the product of the n pairs. For example, if 2n = 4, we have E(X1X2X3X4) = C12C34 + C1324 + C14C23, and similarly, E(XA) = E(XXXXi) = Cucu + CuChi + CuCHI = 3 [E(X2) ]2