Suppose, X, Y, and Z are independent, zero- mean, unit- variance Gaussian random variables.

(a) Using the techniques outlined in Section 6.4.2, find the characteristic function of
W = XY + XZ + YZ.
(b) From the characteristic function found in part (a), find the mean and variance of .
(c) Confirm your answer in part (b) by finding the mean and variance of W directly. In this part, you may want to use the result of the Gaussian moment factoring theorem developed in Exercise 6.18.