Question: 8. Let the joint probability density function of random variables X and Y be bivariate normal. Show that if X = Y , then X

8. Let the joint probability density function of random variables X and Y be bivariate normal. Show that if σX = σY , then X + Y and X − Y are independent random variables.

Hint: Show that the joint probability density function ofX+Y andX−Y is bivariate normal with correlation coefficient 0.

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