(Solution) - Suppose that two random variables X1 and X2 have a -(2025 Original AI-Free Solution)

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Suppose that two random variables X1 and X2 have a bivariate normal distribution, and two other random variables Y1 and Y2 are defined as follows:
Y1 = a11X1 + a12X2 + b1,
Y2 = a21X1 + a22X2 + b2,
Where

Show that Y1 and Y2 also have a bivariate normal distribution.