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Let \(X_1\) and \(X_2\) be the results of rolling two fair six-sided dice.Each die follows a discrete uniform distribution on \(\{1, 2, 3, 4, 5, 6\}\).Let \(S_2 = X_1 + X_2\) be the sum of the two dice.
  1. Find the mean and the variance of a single die roll \(X_1\).
  2. Deduce the mean of \(S_2\).
  3. Deduce the variance of \(S_2\).
  4. Find the standard deviation of \(S_2\).

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