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A player rolls two fair six-sided dice. Let \(X_1\) be the result of the first roll and \(X_2\) the result of the second.
  1. Determine the set of all possible values for the sum \(S_2=X_1+X_2\).
  2. Determine the set of all possible values for the sample mean \(\overline{X}_2=\dfrac{X_1+X_2}{2}\).

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