Question: Two Gaussian random variables, X and Y, are in dependent. Their respective means are 4 and 2, and their respective variances are 3 and 5.

Two Gaussian random variables, X and Y, are in dependent. Their respective means are 4 and 2, and their respective variances are 3 and 5.

(a) Write down expressions for their marginal pdfs.

(b) Write down an expression for their joint pdf.

(c) What is the mean of Z1 = 3X + Y? Z2 = 3X - Y?

(d) What is the variance of Z1 = 3X + Y? Z2 = 3X - Y?

(e) Write down an expression for the pdf of Z1 = 3X + Y.

(f) Write down an expression for the pdf of Z2 = 3X - Y.

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