12 Let the joint probability density function of X and Y be bivariate normal Prove that any linear combination of X and Y, X Y, is a normal random variable Hint Use Theorem 11 7 and the result of Exercise 7, Section 10 5 ...

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12. Let the joint probability density function of X and Y be bivariate normal. Prove that any...

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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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Fundamentals Of Probability With Stochastic Processes

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12. Let the joint probability density function of X and Y be bivariate normal. Prove that any...

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