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6. (6%) Consider this question related to Q3, Q4, and Q5 . Is this statement true:...

6. (6%) Consider this question related to Q3, Q4, and Q5 . Is this statement true: there exist two independent random variables X and Y such that Var [X] = Var [Y] = 1;E[X] = E[Y] = 0, and also Cov [X, Y] = 0? If true, find such example, otherwise prove why this is impossible.

7. (9%) Is it possible that Covariance [X, Y] equals to (a) 0.5 (6%) (b) 5 (3%) or some random variables X and Y. Explain! Note in this question, we do not require X and Y to be independent.

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