Verified solution · Exam P
This Exam P sample reference tests Uniform Distribution. This is a uniform-moment inversion followed by a percentile calculation. The stated second moment forces the first lower endpoint to be 60, making the second interval [75,100] and its 80th percentile 95, so choice E.
Independent solution
Setup
Use the raw second moment formula for a uniform variable whose endpoints are a and 100.
Model
Solve the resulting quadratic and retain the root that forms a valid interval below 100.
Compute
The valid lower endpoint is 60, so the second model begins at 1.25 × 60. Move 80% of the way across that interval.
Answer
The requested percentile is 95.
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Error diagnosis
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Original practice · fully worked
A calibration drift U is uniformly distributed on [a,16], where a is less than 16, and its second raw moment is 112. A correction amount is C=max(U-10,0). Calculate E[C].
The uniform second-moment equation gives the valid lower endpoint a=4. Averaging the positive excess U-10 over the resulting interval [4,16] gives E[C]=1.5 units, so choice B.
Setup
Use the raw second moment of a uniform variable to recover the unknown lower endpoint.
Model
Retain the endpoint that produces a valid ordered support.
Compute
Integrate the positive correction over the portion of the support above the threshold.
Answer
The expected correction amount is 1.50 units.
Keep practicing
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 Uniform Distribution problems
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ActuaryProof. “SOA Exam P Sample Question #257 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
