Worked solution · Exam P
This Exam P sample reference tests Exponential Distribution. This problem asks for an exponential lifetime probability after survival to an earlier age. Memorylessness leaves a fifteen-year residual window, whose failure probability is 0.608394 and choice C.
Independent solution
Setup
Convert the supplied exponential rate to its survival function.
Model
Conditioning on survival to year five turns the upper endpoint into fifteen additional years.
Compute
Evaluate the residual lower-tail probability.
Answer
The conditional probability rounds to 0.608.
Test the method on unseen problems
30 original univariate random variables problems with complete solutions and wrong-choice analysis. Written for Exam P, not copied from the SOA set. One-time $19 PDF.
Error diagnosis
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Original practice · fully worked
A filtration cartridge has survival function S(t)=exp[-(t/8)²] for t≥0, where t is measured in hours. A cartridge is still operating at hour 4. Calculate the conditional probability that it fails by hour 8.
Conditional survival from hour 4 through hour 8 is S(8)/S(4)=exp(-0.75). Its complement is 0.527633, so choice C.
Setup
Write the conditional survival ratio over the observed operating interval.
Model
The squared-time cumulative hazard means the elapsed four hours do not cancel as they would for an exponential lifetime.
Compute
Take the complement of conditional survival to obtain failure by hour eight.
Answer
The conditional failure probability rounds to 0.5276.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 387 Exam P univariate random variables practice problems.
Drill the method: Exam P Conditional Probability problems · Exam P Exponential Distribution problems
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