Theorem by Lindeberg

Lindeberg's Theorem provides conditions under which the sum of many independent, not necessarily identical, random variables behaves similarly to a normal (bell-shaped) distribution as the number of variables grows large. It ensures that if no individual variable has too much influence and their combined variability meets certain criteria, then the overall sum will approximate a Gaussian distribution. This theorem underpins why the normal distribution appears so frequently in nature and statistics, especially when aggregating diverse independent sources of random variation.