Worked solution · Exam P
This Exam P sample reference tests Gamma Distribution. The density kernel is gamma with shape 6 and rate 0.01. Its mean is 6/0.01=600, so choice E is correct.
Independent solution
Setup
Match the power and exponential factor to a gamma density written in shape-rate form.
Model
For a gamma variable with shape alpha and rate beta, the normalizing constant does not need to be found separately to use the mean formula.
Compute
Substitute the identified shape and rate.
Answer
The expected value is 600.
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 sensor's recalibration delay T follows a gamma distribution with shape alpha and scale θ. Field engineers report a mode of 6 minutes and a coefficient of variation of 1/2. Calculate Var(T).
The coefficient of variation gives shape 4, and the mode then gives scale 2. Thus the variance is 4(2²)=16, so choice D is correct.
Setup
Use the gamma coefficient of variation to recover the shape parameter.
Model
For shape greater than one, the gamma mode identifies the scale after the shape is known.
Compute
Recover the scale and then evaluate the gamma variance.
Answer
The delay variance is 16 square minutes.
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 Tail Integral Formula and Expected Value problems
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