Worked solution · Exam P
This Exam P sample reference tests Insurance Payment Variables. This is an expected excess-loss calculation for a uniform loss. A deductible d leaves expected payment (100-d)²⁄²⁰⁰; setting that expression equal to 32 gives a remaining width of 80 and therefore d=20, choice C.
Independent solution
Setup
Let the insurer payment under deductible d be the positive excess above d.
Model
Integrate the payment against the uniform density on the part of the loss interval above d.
Compute
Set the expected payment equal to 32 and retain the feasible root.
Answer
The deductible is 20.
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
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
Original practice · fully worked
A repair loss is uniformly distributed from 0 to 10. Independently of the loss, a service contract uses a deductible of 2 with probability 0.40 and a deductible of 6 with probability 0.60. The contract pays the loss above the selected deductible. Calculate the expected payment.
The expected payments under deductibles 2 and 6 are 3.2 and 0.8. Weighting them by probabilities 0.40 and 0.60 gives 1.76, choice C.
Setup
Use the uniform stop-loss formula at each possible deductible.
Model
Evaluate the two conditional expected payments.
Compute
Average the conditional payments over the independent deductible selection.
Answer
The expected contract payment is 1.760.
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 Uniform Distribution problems
Keep studying
Work through the related free solutions for this topic, review the formulas you used, or keep every current Exam P solution in one searchable PDF.
