Verified solution · Exam P
This Exam P sample reference tests Sums of Independent Random Variables. Independence lets the second component inherit mean 0.8 and variance 1.35 from the stated totals. Its coefficient of variation is √(1.35)/0.8 = 1.45237, so the answer is E.
Independent solution
Setup
Recover the mean of the unobserved component by subtracting component means.
Model
For independent components, the variance of their sum is the sum of their variances.
Compute
Divide the component standard deviation by its mean.
Answer
The coefficient of variation rounds to 1.45.
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Original practice · fully worked
A fabrication shop models two independent random resource loads, X and Y. Their means are 3 and 5 units, and their standard deviations are 1 and 2 units, respectively. A batch cost index is defined by C=2X+Y. Calculate the coefficient of variation of C.
The weighted cost has mean 2(3)+5=11. Independence gives variance 2 squared times 1 squared plus 2 squared, or 8. Therefore its coefficient of variation is √(8)/11=0.2571297, so choice B is correct.
Setup
Apply linearity of expectation to the weighted cost index.
Model
Independence removes the covariance term, while the coefficient on X is squared in the variance.
Compute
Divide the standard deviation of the cost index by its mean.
Answer
The cost-index coefficient of variation rounds to 0.257.
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ActuaryProof. “SOA Exam P Sample Question #634 — Verified Solution.” Verified 2026-07-30.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-30.
