Question: Two jointly Gaussian random variables, X and Y, have means of 1 and 2, and variances of 3 and 2, respectively. Their correlation coefficient is

Two jointly Gaussian random variables, X and Y, have means of 1 and 2, and variances of 3 and 2, respectively. Their correlation coefficient is P_xy = 0.2. A new random variable is defined as Z = 3X + Y. Write down an expression for the pdf of Z.

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