Let a random variable Z be defined in terms of three independent random variables as Z =

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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;

(c) The standard deviation of Z;

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

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