Worked solution · Exam P
This Exam P sample reference tests Uniform Distribution. The first uniform standard deviation gives b=9.60√(12). The second interval then has width 2b-6, so its standard deviation is (2b-6)/√(12)=17.468, which rounds to choice C.
Independent solution
Setup
For a continuous uniform variable, standard deviation equals its support width divided by the square root of twelve.
Model
Use the first interval width to recover the unknown endpoint.
Compute
Form the width of the second support and apply the same uniform formula.
Answer
The second standard deviation rounds to 17.5.
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 dial error U is uniformly distributed on the symmetric interval from -a to a. Its mean absolute error is 4 units. A corrected output is V=3U+2. Calculate the variance of V.
For a symmetric uniform error, E|U|=a/2, so a=8 and Var(U)=a²⁄³=64/3. Scaling by 3 multiplies variance by 9, giving 192 and choice D.
Setup
Use symmetry to evaluate the mean absolute error in terms of the unknown half-width.
Model
Recover the half-width and then the variance of a uniform variable on the symmetric support.
Compute
Apply the affine variance rule; the additive constant does not affect spread.
Answer
The corrected output has variance 192.
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 Uniform Distribution 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.
