Verified solution · Exam P
This Exam P sample reference tests Exponential Distribution. The payment median is positive because the zero-payment probability is below one half. The corresponding loss threshold is the loss median 4 ln(2), so subtracting the deductible gives 1.7726, choice A.
Independent solution
Setup
Write the ordinary-deductible payment as a positive-part transformation of the loss.
Model
For a positive candidate median y, the event Y at most y is the same as X at most y+1.
Compute
Set the payment distribution function equal to one half and solve.
Answer
The median payment rounds to 1.77.
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Original practice · fully worked
A battery lifetime X is exponentially distributed with mean 4 hours. A diagnostic logger activates if the battery remains operating after hour 2 and then records for at most 3 additional hours. Given that the logger activates, calculate its expected recording time.
Conditional on reaching hour 2, exponential memorylessness makes the remaining lifetime exponential with mean 4. Recording at most 3 additional hours gives expectation 4(1-exp(−3/4))=2.1105, choice C.
Setup
Write the capped recording duration and condition on logger activation.
Model
Memorylessness makes the remaining lifetime a fresh exponential variable Z with mean 4.
Compute
Use the survival-integral formula for the limited mean.
Answer
Given activation, the expected recording time is approximately 2.1105 hours.
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Drill the method: Exam P Exponential Distribution problems
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ActuaryProof. “SOA Exam P Sample Question #215 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
