Central Limit Theorem/Conditions

Conditions under which Central Limit Theorem holds

The Central Limit Theorem holds under the following conditions:

• The variance of any one of the contributory random variables does not dominate.
• The samples are not from the Cauchy distribution, as from Cauchy Distribution has no Finite Moments, the Cauchy distribution has no expectation.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): central limit theorem
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): central limit theorem