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Zorluk: KolayLaw of Large Numbers

An insurance company expands its auto insurance pool from 500 policyholders to 50,000 policyholders who share similar driving characteristics. According to the law of large numbers, what is the primary benefit of this expansion for the insurer?

  1. It increases the accuracy of predicting total future losses, even though individual losses remain unpredictable.Cevap
  2. B
    It converts the drivers' pure risks into speculative risks, guaranteeing that the insurer will make a financial gain.
  3. C
    It allows the insurer to handle the exposures through risk avoidance rather than risk transfer.
  4. D
    It automatically transfers the insurer's direct liability for paying these claims to a reinsurance company.

Cevap

It increases the accuracy of predicting total future losses, even though individual losses remain unpredictable.
The law of large numbers states that as the number of homogeneous (similar) exposure units increases, the statistical predictability of future losses improves. This allows the insurer to accurately forecast total aggregate claims for the group, even though it is impossible to predict which specific driver will have an accident.

Adım Adım Çözüm

1
Identify the core concept being tested in the scenario.
The scenario describes increasing the number of similar exposure units (from 500 to 50,000 policyholders).
Recognizing the components of the scenario points directly to the definition of the law of large numbers.
2
Apply the definition of the law of large numbers to the scenario.
As the number of similar exposure units increases, the actual losses will more closely approach the expected losses.
This mathematical principle is what allows insurers to set accurate rates based on expected aggregate losses.
3
Evaluate the limitations of the law of large numbers.
While total losses become highly predictable, the insurer still cannot predict exactly which individual policyholder will experience a loss.
The law only applies to the aggregate pool, not to individual independent events.

Anahtar Kavram

The Law of Large Numbers
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Konular

Law of Large Numbers

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