Verified solution · Exam P
This Exam P sample reference tests Exponential Distribution. This is the expected excess of an exponential loss above a deductible. The probability of reaching the deductible is exp(−3/10), and memorylessness leaves mean excess 10, so expected payment is 10 exp(−0.3)≈7.41 and choice D.
Independent solution
Setup
Represent the insurer payment as the positive excess above the deductible.
Model
A positive payment requires survival beyond three, and the exponential residual loss then has its original mean.
Compute
Multiply the payment probability by the conditional mean payment.
Answer
The expected claim payment is approximately 7.41.
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Original practice · fully worked
A repair is minor with probability 0.30 and major with probability 0.70. Conditional on a minor repair, loss X is exponential with mean 4 units; conditional on a major repair, X is exponential with mean 10 units. A service plan pays the amount above a deductible of 5 units. Calculate the expected plan payment.
For an exponential loss with mean μ, expected payment above five is μe to the power (−5/μ). Weighting the minor and major values by 0.30 and 0.70 gives 0.30(4 exp(−5/4))+0.70(10 exp(−1/2))≈4.590 and choice D.
Setup
Use the exponential stop-loss expectation separately within each repair class.
Model
Average the two conditional payment means with their repair-class probabilities.
Compute
Evaluate the minor and major contributions and add them.
Answer
The expected service-plan payment is approximately 4.590.
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These references share syllabus concepts or sit nearby in the official sequence. All 388 Exam P univariate random variables practice problems.
Drill the method: Exam P Exponential Distribution problems
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ActuaryProof. “SOA Exam P Sample Question #337 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
