limit theorems

Limit theorems are mathematical principles that describe the typical behavior of a sequence of numbers or random variables as they grow large or as we observe more data. They show that, under certain conditions, the average or sum of many small, independent parts tends to follow a predictable pattern—like a bell curve in the case of the Central Limit Theorem. Essentially, limit theorems tell us that despite variability in individual data points, the overall behavior becomes stable and predictable when enough data or trials are considered.