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X and Y are zero mean independent Gaussian random variables with standard deviations 1 and 2 respectively. Let Z = aX + bY + c

X and Y are zero mean independent Gaussian random variables with standard deviations 1 and 2 respectively. Let Z = aX + bY + c where c does not equal zero.

a. Find the characteristic function of Z.

b. Is Z a Gaussian Random Variable? How do you know?

c. Find the mean and the variance of Z.

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