Society of Actuaries (SOA) PA Practice Exam

What does the Law of Large Numbers describe?

1. The accuracy of models used in statistical predictions

2. The relationship between sample size and parameter estimation

3. The convergence of average results to the expected value with trials

4. The effect of randomness in small sample sizes

The correct answer is: The convergence of average results to the expected value with trials

The Law of Large Numbers is a statistical theorem that states that as the number of trials in a random experiment increases, the sample average will converge to the expected value of the underlying distribution. This means that if you repeatedly conduct an experiment—such as flipping a coin or rolling a die—the average outcome of those trials will get closer to the theoretical average as you perform more and more trials. Understanding this principle is crucial for actuaries and statisticians as it underpins many of the methods used in risk assessment and probability. The law assures that larger sample sizes will provide more reliable estimates of population parameters, which is foundational for effective decision-making based on statistical data. In contrast, while the accuracy of models, the relationship between sample size and parameter estimation, and the impact of randomness in small sample sizes are all important concepts in statistics, they do not encapsulate the core idea of the Law of Large Numbers as effectively as the concept of convergence of average results toward the expected value.