Verified solution · Exam P
This Exam P sample reference tests Exponential Distribution. The exponential memoryless property makes the elapsed event-free period irrelevant to the residual wait. Subtracting the survival probability beyond 25 days from the survival probability beyond 5 days gives 0.527656, which rounds to 0.53 and selects choice D.
Independent solution
Setup
Let W denote the additional waiting time from the present. The original exponential mean determines its rate.
Model
By memorylessness, the residual wait is exponential with the same mean despite the elapsed quiet period.
Compute
The probability of landing between the two residual-time bounds is the difference of their survival probabilities.
Answer
The requested probability rounds to 0.53.
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Original practice · fully worked
At a remote observatory, the time until a calibration routine completes is exponential with mean 8 minutes. An independent safety watchdog stops the routine after an exponential time with mean 12 minutes. Both clocks start together. Calculate the probability that calibration finishes first and finishes more than 3 minutes after the start.
The two clocks race at combined rate 5/24. Integrating the calibration completion density after minute three while the watchdog survives gives (3/5) exp(−5/8)=0.321157, so choice B is correct.
Setup
Let C be the calibration completion time and W the independent watchdog time. Convert their means to rates.
Model
For calibration to finish first at time t, its density contributes while the watchdog must survive through t.
Compute
Combine the exponential rates and evaluate the tail integral.
Answer
The delayed calibration-win probability rounds to 0.321.
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 Exponential Distribution problems
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ActuaryProof. “SOA Exam P Sample Question #621 — Verified Solution.” Verified 2026-07-30.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-30.
