Match each underwriting scenario or statistical concept related to the Law of Large Numbers with its corresponding actuarial outcome or principle.
- Adding 50,000 similar single-family homes to an existing property insurance portfolioImproves the accuracy of aggregate loss predictions for the insurer
- The statistical variance between projected claims and actual experienced claimsDiminishes as the total number of exposure units increases
- Attempting to determine exactly which specific policyholder will file a claim this yearRemains impossible regardless of how large the insured group becomes
- Grouping commercial delivery fleets and personal sedans into a single rating poolPrevents accurate rate-setting because the exposure units are not homogeneous
Cevap
The scenarios map as follows: Adding similar homes improves aggregate prediction accuracy. Statistical variance diminishes as exposure units increase. Predicting an individual's claim remains impossible regardless of pool size. Mixing commercial and personal vehicles prevents accurate rate-setting due to lack of homogeneity.
Each scenario illustrates a distinct facet of the Law of Large Numbers: the necessity of large sample sizes to reduce statistical variance, the rigid requirement for homogeneity among exposure units, and the distinction between reliable group predictability versus persistent individual uncertainty.
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Anahtar Kavram
The Law of Large Numbers requires a large volume of homogeneous exposure units to reduce statistical variance and accurately predict aggregate losses, but it cannot be used to predict individual losses.