Worked solution · Exam P
This Exam P sample reference tests Deductible Payments. Because the loss is already above the fixed deductible, the payment is the affine transform p(X-d). Subtracting d does not change variance and multiplying by p multiplies variance by p², so the result is p²v and choice B is correct.
Independent solution
Setup
Write the payment as a constant shift followed by a proportional scaling.
Model
Variance is invariant under an additive constant and is multiplied by the square of a scale factor.
Compute
Apply the affine-variance rule to the payment.
Answer
The deductible changes the mean but not the variance; the proportional factor supplies the square.
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 laboratory converts a raw measurement L into a quality score Q=0.6(L-20). The standard deviation of Q is 9. Calculate Var(L).
The converted score has variance 81, while Var(Q)=0.6²Var(L). Therefore Var(L)=81/0.36=225 and choice E is correct.
Setup
Square the reported score standard deviation.
Model
The shift by 20 has no variance effect, and the multiplier 0.6 is squared.
Compute
Invert the scale relationship.
Answer
The raw measurement variance is 225.
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 Variance problems
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