Worked solution · Exam P
This Exam P sample reference tests Uniform Distribution. For a continuous uniform variable, the mean is the midpoint and the 75th percentile is one quarter of the support width above that midpoint. The six-unit separation therefore gives width 24 and variance 24²⁄¹²=48, so choice C is correct.
Independent solution
Setup
Let a be the lower endpoint and let w be the positive width of the uniform support.
Model
The 75th percentile is three quarters of the way across the support. Subtracting the midpoint equation removes the unknown lower endpoint.
Compute
Recover the support width from the six-unit percentile gap, then apply the continuous-uniform variance formula.
Answer
The variance is 48.
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.
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Original practice · fully worked
A timing calibration error D is uniformly distributed on a symmetric interval centered at zero. Forty percent of calibration errors fall between -2 milliseconds and 2 milliseconds. Calculate Var(D).
If the support is [-h,h], the central interval has probability 4/(2h)=0.40, so h=5 and the full width is 10. The variance is 10²⁄¹²=25/3, which rounds to 8.33 and selects choice C.
Setup
Write the unknown symmetric support using its positive half-width h.
Model
Uniform probability is an interval-length ratio. The reported central interval has length four.
Compute
Solve for the half-width and use the variance of a uniform variable on a symmetric interval.
Answer
The calibration-error variance is approximately 8.33 square milliseconds.
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 · Exam P Uniform Distribution problems
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