This result is closely related to the Gram-Charlier and Edgeworth expansions in terms of cumulants.
This result is closely related to the Gram-Charlier and Edgeworth expansions in terms of cumulants. Lindeberg showed that a weaker condition is sufficient in a variant of this statement that replaces the requirement of identical distributions with the Lyapunov condition on third moments about the mean. The Cauchy distribution does not satisfy the conditions of this theorem, and in fact has a sample variance that is independent of the sample size. FTP, name this theorem stating that any sum of "I I D" random variables converges in distribution to the normal distribution.
This result is closely related to the Gram-Charlier and Edgeworth expansions in terms of cumulants.
{Central Limit Theorem} or {CLT}