Question: 13. Let the joint probability density function of X and Y be bivariate normal. Prove that any linear combination of X and Y , X

13. 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 6, Section 10.5.

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