Multivariate distributions: Expected value of a sum -- Example 2

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Multivariate distributions: Expected value of a sum -- Example 2
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Confused as why (n * (2/(2n-1))) is valid? (2/(2n-1)) is valid for first couple, shouldn't the remaining couples is (2/(2n-3)), (2/(2n-5)), (2/(2n-7))...?

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