Worked solution · Exam P
This Exam P sample reference tests Variance. Independence removes the covariance term. Squaring the coefficients gives variance 9(1)+1(2)=11, official choice D.
Independent solution
Setup
The additive constant has no effect on variance. Independence also removes the covariance cross term.
Model
Each component variance is multiplied by the square of its coefficient, including the negative coefficient on the second component.
Compute
The two variance contributions are 9 and 2, giving total variance 11.
Answer
The independent linear combination has variance 11, selecting choice D.
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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
Independent measurements U and V have variances 4 and 9. A laboratory index is W=-2U+3V+12. Find Var(W).
The offset disappears and the squared coefficients give 4(4)+9(9)=97.
Setup
The calibration offset does not affect variance, and independence removes any covariance term.
Model
Multiply each component variance by the square of its coefficient. The negative sign on the first component disappears when squared.
Compute
The two contributions are 16 and 81, giving total variance 97.
Answer
The laboratory index has variance 97, selecting choice C.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 140 Exam P multivariate random variables practice problems.
Drill the method: Exam P Variance problems · Exam P Independence problems
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