Worked solution · Exam P
This Exam P sample reference tests Variance and Standard Deviation. Independence makes the four cost variances additive. Their sum is 8.25, and its square root is 2.872281, which rounds to 2.9 and choice C.
Independent solution
Setup
Let T denote the sum of the four plant costs.
Model
Use independence to add variances rather than standard deviations.
Compute
Evaluate the aggregate variance and convert back to standard-deviation units.
Answer
The total-cost standard deviation rounds to 2.9.
Test the method on unseen problems
30 original multivariate 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
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Original practice · fully worked
An underwater microphone's centered measurement noise is the sum of three independent sources. Their standard deviations are 4, 5, and 10 millipascals. What fraction of the total noise variance is attributable to the third source?
The three independent variance contributions are 16, 25, and 100. The third source therefore contributes 100 of the total 141 variance units, or 0.709220, which is choice E.
Setup
Convert each source's standard deviation to a variance contribution.
Model
Independence removes cross-covariance terms from the total variance.
Compute
Divide the third contribution by the aggregate variance.
Answer
The third source accounts for approximately 0.709 of total variance.
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