What does the Law of Large Numbers state?

The Law of Large Numbers is a fundamental principle in statistics and probability theory that states as the number of exposure units (or trials) increases, the actual results will tend to converge on the expected results. This principle is crucial in fields such as insurance where the accuracy of predicting future claims improves as more data is collected.

When an insurer has a larger pool of policies, the randomness of claims balances out, allowing for more accurate estimations of the overall risk and expected losses. In essence, with a higher number of exposure units—like insurance policies—the insurer can better predict future claims and thus set proper premiums, thereby enhancing prediction accuracy. This reduces the variance of loss estimates and leads to more stable and reliable financial outcomes for the insurance company.

The other choices do not directly express the essence of the Law of Large Numbers. High coverage in policies does not inherently influence overall costs in a straightforward manner as there are numerous factors at play in actuarial calculations. The statement about independent units creating uncertainty misrepresents the Law of Large Numbers, as it emphasizes aggregation reducing uncertainty. Finally, the idea that more policies lead to increased losses is contrary to the foundational concept of the Law of Large Numbers, which supports the idea that more data typically yields better prediction and