Let X be a normal random variable with mean vector r and covariance matrix r,s.

Let X be a normal random variable with mean vector λ

r and covariance matrix λ

r,s. Define h

r = h r (x; λ), h rs (x; λ),…

to be the Hermite tensors based on the same normal distribution, i.e., and so on as in (5.7). Show that the random variables h

r (X), h rs (X), h rst (X),…

have zero mean and are uncorrelated.