Worked solution · Exam P
This Exam P sample reference tests Discrete Random Variables. For a nonnegative integer count, the expectation is the sum of its positive-threshold survival probabilities. Evaluating the five stated tails gives 1.12565, which rounds to 1.1 and choice B.
Independent solution
Setup
Use the tail-sum identity for a count supported from zero through five.
Model
Insert the supplied square-root survival formula.
Compute
Evaluate and add the five survival values.
Answer
The expected number of defective parts rounds to 1.1.
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 device has a failure count N between zero and four. Its probabilities of at least one, two, three, and four failures are 0.60, 0.35, 0.15, and 0.05. A service visit costs 12 dollars plus 5 dollars per failure. Calculate the expected service cost.
Adding the four tail probabilities gives an expected failure count of 1.15. The affine service charge therefore has expectation 12 plus five times 1.15, or 17.75 dollars. This is choice D.
Setup
Apply the tail-sum identity to the bounded failure count.
Model
Write the service cost as an affine function of the count.
Compute
Use linearity of expectation.
Answer
The expected service cost is 17.75 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 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.
