Question: 12. Let the joint probability density function of X and Y be bivariate normal. Prove that any linear combination of X and Y, X +

12. Let the joint probability density function of X and Y be bivariate normal. Prove that any linear combination of X and Y, αX + βY, is a normal random variable.

Hint: Use Theorem 11.7 and the result of Exercise 7, Section 10.5.

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