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In a city election, it is known that \(45\pourcent\) of the population intends to vote for Candidate A. A pollster surveys a random sample of \(n=100\) voters.
Let \(X_i\) be the random variable representing the response of the \(i\)-th person surveyed.
  1. Define the random variable \(X_i\) using the convention \(1\) for "Success" and \(0\) for "Failure".
  2. State the probability distribution of \(X_i\).
  3. What does the sum \(S_{100} = \sum_{i=1}^{100} X_i\) represent in this context?

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