# Question: Suppose X Y and Z are independent zero mean unit

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.

(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.

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