How to prove the independence of the functions of two random variables distributed with multivariate normal.

Asked Sep 25 '21 at 19:40

Active Sep 25 '21 at 19:40

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I have to prove this statement on one of my problem sets:

If X1 and X2 are independent random variables, both distributed as N (0,1), then X1+X2 and X1−X2 are independent random variables.

I know that I have to use the properties of the multivariate normal distribution, but I don't know how to.

Thank you in advance.

asked Sep 25 '21 at 19:40

DPedro

Have you tried using the definition? – Jacky Chong Sep 25 '21 at 19:43
Duplicate of this more general question of which the present question is the special case $n=1$. – Dilip Sarwate Sep 25 '21 at 19:59
I will check your answer!! Thank you !!! – DPedro Sep 25 '21 at 20:46

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