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Let \(X_1\) and \(X_2\) be the result of two coin flips, where \(X_i=1\) if the \(i\)-th coin lands on Head and \(0\) otherwise (fair coin).Let \(\overline{X}_2 = \frac{X_1 + X_2}{2}\) be the sample mean.
What are the possible values of \(\overline{X}_2\)?
Find the probability distribution of \(\overline{X}_2\).
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