Which factor is essential for the law of large numbers to make losses predictable?

Which factor is essential for the law of large numbers to make losses predictable?

• A. A large number of similar exposure units
• B. A small number of large exposure units
• C. The exact same exposure units across time
• D. High variation in losses

Answer: (A)

The key idea is that the law of large numbers makes outcomes more predictable when you have a big pool of similar exposure units. As the number of exposures grows, the average loss across those exposures tends to approach the expected loss. The randomness of individual losses cancels out over many units, so the overall loss experience becomes more stable and predictable. That’s why a large number of similar exposure units is essential: it provides enough observations for the average to converge to the expected value. If you only have a few exposures, random fluctuations dominate and the average loss can swing a lot, making predictions unreliable. Repeating the same units over time isn’t necessary for LLN to apply; what matters is the size of the current pool of similar risks and the assumption that those risks are independent and drawn from roughly the same distribution. High variation in losses would make predictability worse, not better, so that choice goes against the law’s effect.

The key idea is that the law of large numbers makes outcomes more predictable when you have a big pool of similar exposure units. As the number of exposures grows, the average loss across those exposures tends to approach the expected loss. The randomness of individual losses cancels out over many units, so the overall loss experience becomes more stable and predictable. That’s why a large number of similar exposure units is essential: it provides enough observations for the average to converge to the expected value.

If you only have a few exposures, random fluctuations dominate and the average loss can swing a lot, making predictions unreliable. Repeating the same units over time isn’t necessary for LLN to apply; what matters is the size of the current pool of similar risks and the assumption that those risks are independent and drawn from roughly the same distribution. High variation in losses would make predictability worse, not better, so that choice goes against the law’s effect.