Given a sequence of independent random variates , , ..., if
and

then

This means that if the Lindeberg Condition holds for the sequence of variates , ..., then the Variance of an individual term in the sum of is asymptotically negligible. For such sequences, the Lindeberg Condition is Necessary as well as Sufficient for the Lindeberg-Feller Central Limit Theorem to hold.

**References**

Zabell, S. L. ``Alan Turing and the Central Limit Theorem.'' *Amer. Math. Monthly* **102**, 483-494, 1995.

© 1996-9

1999-05-26