Central Limit Theorem

A probabilistic result stating that suitably normalized sums (or averages) of many independent, identically distributed random variables with finite variance converge in distribution to a Gaussian (normal) law as the number of terms grows without bound.

A family of limit results stating that suitably normalized sums (or averages) of many independent (or weakly dependent) random variables with finite variance converge in distribution to a Gaussian (normal) law as the number of terms tends to infinity, under mild regularity conditions (e.g., Lindeberg or Lyapunov conditions).