Question: A die is rolled twice. Let X equal the sum of the outcomes, and let Y equal the firstoutcome minus the second. (a) Are X

A die is rolled twice. Let X equal the sum of the outcomes, and let Y equal the firstoutcome minus the second. (a) Are X and Y independent random variables? (b) Compute Cov(X, Y). Note: We know that X and Y being independent implies Cov(X, Y) = 0. Thisproblem shows the converse is not true, i.e. Cov(X, Y ) = 0 does not imply X andY are independent.

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