Massachusetts Life Producer Practice Exam

Which of these statements is NOT a characteristic of the law of large numbers?

1. Rates can be calculated to compensate for losses

2. Increased number of instances improves predictability

3. Greater data leads to better forecasts

4. Insurance risk remains constant regardless of sample size

The correct answer is: Rates can be calculated to compensate for losses

The concept of the law of large numbers is fundamental to insurance and statistical analysis, emphasizing that as the number of instances or trials increases, the actual results will converge to the expected results. The statement that rates can be calculated to compensate for losses is an essential feature of how insurance operates, rather than a characteristic of the law of large numbers itself. The law of large numbers primarily focuses on the relationship between the size of a sample and the accuracy of predictions, rather than the method of rate calculation. In contrast, the other statements capture key aspects of the law of large numbers. As the number of instances increases, predictability improves because patterns in data become clearer, leading to more accurate estimations (this verification of statistical probabilities is central to risk assessment in insurance). Similarly, the idea that greater data leads to better forecasts aligns with the principle that larger sample sizes generally yield results that are closer to the overall expected outcome. The constant nature of insurance risk regardless of sample size is not true according to the law; rather, the variability of outcomes diminishes as more data is considered. Thus, the correct identification of the statement about rate calculations as unrelated to the law of large numbers highlights the distinction between operational practices in insurance and theoretical statistical principles.