The Law of Large Numbers (LLN) is a fundamental theorem in probability theory that describes how the average of a large number of independent and identically distributed (i.i.d.) random variables tends to converge to the expected value as the number of trials increases. There are two main versions of the LLN: the Weak Law of Large Numbers (WLLN) and the Strong Law of Large Numbers (SLLN).

The WLLN states that as the number of trials increases, the probability that the sample mean deviates from the expected mean by a certain amount approaches zero. This means that with a sufficiently large number of trials, the sample mean will be close to the expected value with high probability ²³.

On the other hand, the SLLN asserts that the sample average will converge to the expected value almost surely, which is a stronger form of convergence compared to the WLLN ¹⁴. The LLN is crucial in various fields, including statistics, insurance, and artificial intelligence, as it underpins the reliability of predictions and estimations based on large datasets.