Worked solution · Exam P
This Exam P sample reference tests Deductible Payments. A deductible between 60 and 200 removes the smallest claim and reduces the other two payments dollar for dollar. Setting the resulting expected payment 40-0.06d equal to 30 gives d=166.67, choice C.
Independent solution
Setup
Let d be the ordinary deductible and write the expected payment from the three mutually exclusive loss amounts.
Model
A target payment of 30 requires a deductible above 60 but below 200, so only the two larger losses pay.
Compute
Equate the expected payment to its target and verify the assumed deductible interval.
Answer
The deductible lies between 150 and 200.
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 cost follows an exponential distribution with mean 1000. A plan pays the amount of each repair cost above an ordinary deductible d, with no upper limit. Determine d if the expected plan payment per repair is 300.
For an exponential cost with mean 1000, the expected excess over d is 1000 exp(-d/1000). Equating this to 300 gives d=1203.97, choice C.
Setup
Use the exponential survival function to express the expected excess payment.
Model
Evaluate the tail integral and set it equal to the target payment.
Compute
Take logarithms and solve for the deductible.
Answer
The required deductible rounds to 1204.
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 Tail Integral Formula and Expected Value 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.
