Verified solution · Exam P
This Exam P sample reference tests Exponential Distribution. Exponential memorylessness resets the lifetime clock at the known survival time. The remaining interval is 0.30, and a mean of 0.50 gives rate 2, so the conditional survival probability is exp(-0.60)=0.548812 and choice D.
Independent solution
Setup
Convert the supplied exponential mean to a rate.
Model
Use memorylessness to replace the conditional lifetime with survival through only the additional interval.
Compute
Evaluate the exponential survival function at the remaining duration.
Answer
The conditional probability rounds to 0.549.
Continue without hunting through PDFs
The searchable 3108-page manual includes this complete solution, its error analysis, and one original worked variant for every active reference.
Error diagnosis
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
Original practice · fully worked
A sterilization cycle has an exponential duration with mean 5 hours. At hour 4 the cycle is still running. A maintenance agreement charges 20 credits if the cycle finishes by hour 7 and 80 credits if it finishes after hour 7. Calculate the conditional expected charge.
Memorylessness makes the chance of running beyond hour 7 equal to exp(-3/5)=0.548812 after the observation at hour 4. Weighting the 20- and 80-credit charges gives 52.928698, so choice E.
Setup
Let R be the residual duration after the cycle is observed running at hour four.
Model
By memorylessness, the residual is exponential with the original five-hour mean.
Compute
Weight the two possible agreement charges by the conditional completion cases.
Answer
The conditional expected charge is approximately 52.929 credits.
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 Conditional Probability problems · Exam P Exponential Distribution problems
Continue in syllabus order
The 3108-page Probability Proof Manual reorganizes 718 verified Exam P solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.
ActuaryProof. “SOA Exam P Sample Question #267 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
