Verified solution · Exam P
This Exam P sample reference tests Discrete Random Variables. This is an expected-payment calculation using linearity of expectation. The two benefit components have expectations 32.50 and 70.00, for a total of 102.50 and choice B.
Independent solution
Setup
Let F and R be the two annual treatment counts. First calculate their expected values from the supplied mass functions.
Model
The annual benefit is the sum of the fully covered lower-cost treatment and the partially covered higher-cost treatment.
Compute
Apply linearity; no assumption about dependence between the two counts is needed.
Answer
The expected annual payment is 102.50.
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Original practice · fully worked
A cooperative classifies leased equipment as light-use with probability 0.75 and heavy-use with probability 0.25. The conditional expected numbers of replacement units are 1.2 and 3.6, respectively. A contract reimburses 40 credits per replacement unit and adds a 90-credit calibration allowance for heavy-use equipment. Calculate the expected reimbursement.
Averaging the two conditional replacement counts gives 1.8 units and 72 credits of unit reimbursement. The heavy-use allowance contributes 22.5 more, for 94.5 credits and choice D.
Setup
Let K be the replacement-unit count and H indicate the heavy-use class. Average the two conditional count means.
Model
Write the contract payment as the unit reimbursement plus the class-specific allowance.
Compute
Evaluate the two expected payment components.
Answer
The expected reimbursement is 94.50 credits.
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These references share syllabus concepts or sit nearby in the official sequence. All 388 Exam P univariate random variables practice problems.
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ActuaryProof. “SOA Exam P Sample Question #255 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
