Q12Section I (Objective (Q1–Q80))12 of 79

Distribution Theory — pdf of a linear combination of correlated normals

Suppose $X$ and $Y$ are zero-mean jointly normally distributed random variables such that $\sigma_X^2=4$ , $\sigma_Y^2=\frac{17}{9}$ , $E(XY)=2$ . If $Z=2X-3Y$ , then what is the pdf of $Z$ ?

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