Verified solution · Exam P
This Exam P sample reference tests Continuous Random Variables. This problem normalizes an inverse-square density above its lower endpoint. The resulting survival function is 100/x, so setting the survival probability to one half gives median 200 and choice D.
Independent solution
Setup
Write the proportional density with constant c and normalize it over its unbounded support.
Model
Integrating the normalized density above a threshold gives a particularly simple survival function.
Compute
A median leaves one half of the probability above it.
Answer
The median loss is 200.
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Original practice · fully worked
A signal amplifier has random gain G such that ln(G) is uniformly distributed between ln(2) and ln(32). Calculate the median of G.
A monotone logarithm preserves percentile order. The midpoint of the log interval is ln(8), so the median gain is 8 and choice C.
Setup
Let U=ln(G). Its median is the midpoint of its uniform support.
Model
Combine the logarithms and then transform back through the increasing exponential function.
Compute
Exponentiating the midpoint gives the geometric mean of the two gain endpoints.
Answer
The median amplifier gain is 8.
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ActuaryProof. “SOA Exam P Sample Question #395 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
