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Convergence in Distribution

A sequence of random variables \(X_n\) with cumulative distribution functions \(F_n\) converges in distribution to \(F\) if: \[ \lim_{n\rightarrow \infty} F_n(x) = F(x) \] for all \(x\). That is, \(F_n\) converges pointwise to \(F\).

This is the convergence used in the central limit theorem.