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The Law of Large Numbers is a fundamental principle in probability theory and statistics. It states that as the number of independent, identically distributed random experiments increases, the relative difference between the empirical probability of an event and its theoretical probability converges to zero.
There are two main formulations of the Law of Large Numbers:
Weak Law of Large Numbers (WLLN):
Strong Law of Large Numbers (SLLN):
The Law of Large Numbers has broad applications in various fields, including statistics, actuarial science, finance, and machine learning. It underscores the stability of statistical estimates when the sample size is large and forms the basis of many probabilistic models.