Worked solution · Exam P
This Exam P sample reference tests Variance. The payment occurs with probability 0.48-0.05=0.43, so it is 1000 times a Bernoulli variable with parameter 0.43. Its standard deviation is 1000 times the square root of 0.43(0.57), or 495.076, which gives choice D.
Independent solution
Setup
Use the two cumulative probabilities to isolate the survival interval that triggers payment.
Model
The contract payment has two possible values.
Compute
Scale the Bernoulli variance and take its square root.
Answer
The standard deviation rounds to 495.
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 delivery contract pays a credit of 0 dollars for an early arrival, 400 dollars for an arrival inside the target window, and 900 dollars for a late arrival. The three outcomes have probabilities 0.18, 0.47, and 0.35, respectively. Calculate the standard deviation of the credit.
The first two credit moments are 503 and 358700. Subtracting the squared mean gives variance 105691, whose square root is 325.102, so choice B.
Setup
Calculate the mean across the three mutually exclusive credit levels.
Model
Use the second-moment identity for variance.
Compute
Subtract the squared mean and take the square root.
Answer
The credit standard deviation rounds to 325.1 dollars.
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
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.
