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Let (X, Y ) be Bivariate Normal, with X and Y marginally N (0, 1) and with correlation

Chapter 7, Problem 71

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QUESTION:

Let (X, Y ) be Bivariate Normal, with X and Y marginally N (0, 1) and with correlation between X and Y . (a) Show that (X + Y,X Y ) is also Bivariate Normal. (b) Find the joint PDF of X + Y and X Y (without using calculus), assuming 1 <

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QUESTION:

Let (X, Y ) be Bivariate Normal, with X and Y marginally N (0, 1) and with correlation between X and Y . (a) Show that (X + Y,X Y ) is also Bivariate Normal. (b) Find the joint PDF of X + Y and X Y (without using calculus), assuming 1 <

ANSWER:

Step 1 of 3

Given that,

Let  be Bivariate Normal, with X and Y marginally N (0, 1) and with correlation  between X and Y.

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