ScholarMatic: Explanation & Answer
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Show transcribed image text Let (X,Y) have a Bivariate Normal distribution with parameters mu X, mu Y, sigma X, sigma Y, and rho. Show that aX + bY + c has a Normal distribution (where a, b, c are real numbers with a 0 or b 0). That is, any linear combination of the components of a Bivariate Normal vector is a Normal random variable.
Let (X,Y) have a Bivariate Normal distribution with parameters mu X, mu Y, sigma X, sigma Y, and rho. Show that aX + bY + c has a Normal distribution (where a, b, c are real numbers with a 0 or b 0). That is, any linear combination of the components of a Bivariate Normal vector is a Normal random variable.
ScholarMatic: Explanation & Answer
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