Question: Let a random variable Z be defined in terms of three independent random variables as Z = 2X 1 + 4X 2 + 3X 3

Let a random variable Z be defined in terms of three independent random variables as Z = 2X₁ + 4X₂ + 3X₃, where the means of X₁, X₂, and X₃ are -1, 5, and -2, respectively, and their respective variances are 4, 7, and 1.

Find the following:

(a) The mean of Z;

(b) The variance of Z;

(d) The pdf of Z if X₁, X₂, and X₃ are Gaussian.

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