Society Of Actuaries (SOA) Actuarial Certification Exam

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An insurance company covers losses up to $10,000 per claim. If the probability distribution of losses is: P(X≤10,000)=0.7, P(X>10,000)=0.3, and the average claim for losses exceeding $10,000 is $15,000, what is the expected claim amount?

$$9,000 $$9,500 $$10,000 $$10,500

Correct Answer:

$$9,500

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