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Let \(X_1, X_2, X_3\) be the results of flipping a fair coin three times.We define \(X_i = 1\) if the coin lands on Heads, and \(X_i = 0\) otherwise.This follows a Bernoulli distribution with \(p=0.5\).Let \(S_3 = X_1 + X_2 + X_3\) be the total number of Heads.
  1. Find the mean and the variance of a single coin flip \(X_1\).
  2. Deduce the expectation (mean) of \(S_3\).
  3. Deduce the variance of \(S_3\).
  4. Find the standard deviation of \(S_3\).

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