Please answer and explain why each is true or false thoroughly. Thank you! True

Question

Please answer and explain why each is true or false thoroughly. Thank you!

True or False? If X & Y are jointly Gaussian, then each of them is Gaussian. If X & Y are Gaussian, they may not be jointly Gaussian. If X & Y are independent & Gaussian, they are jointly Gaussian. If X & Y are Gaussian, their sum may not be Gaussian. If X & Y are independent & Gaussian, their sum is Gaussian. If X & Y are uncorrelated & Gaussian, they may not be independent. If X & Y are uncorrelated & jointly Gaussian, they are independent.

Explanation / Answer

ANSWERS: Gaussian distribution means Normal distribution

1) TRUE (Marginals are also gaussian)

2) TRUE

3) TRUE

4) FALSE

5) TRUE

6) FALSE

7) TRUE

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