Verified solution · Exam P
This Exam P sample reference tests Gamma Distribution. The mean and variance identify gamma shape 2 and scale 3. Its survival probability at 4 is exp(-4/3)(1+4/3)=0.615060, which rounds to 0.62 and choice E.
Independent solution
Setup
Write the gamma moment equations in shape-scale form.
Model
Divide the variance by the mean to obtain the scale, then recover the shape.
Compute
Use the closed-form survival function for an integer shape of two.
Answer
The upper-tail probability rounds to 0.62.
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Original practice · fully worked
Two independent processing times X and Y have gamma distributions with a common scale of 4. Their shape parameters are 2 and 3, respectively. Calculate the probability that X exceeds Y.
For independent gamma variables with a common scale, U=X/(X+Y) is Beta(2,3). Thus P(X>Y)=P(U>1/2)=5/16=0.3125, choice C.
Setup
Transform the two common-scale gamma variables to their share of the total.
Model
The event X greater than Y is equivalent to the share U exceeding one half.
Compute
Integrate the beta density over the upper half of its support.
Answer
The probability that X finishes later is 0.3125.
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Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
