This paper is a small note on the notation :q(X):, for the Wick
ordering of polynomials q of random variables X=(X1,…,Xn), as
introduced by Segal in [6]. We argue that expressing q(X) as another
polynomial p of a different set of random variables Y=(Y1,…,Ym),
does not give rise to a different Wick ordered random variable :p(Y):, provided the new random variables Yj are linear combinations of the
Xi's