Worked solution · Exam P
This Exam P sample reference tests Poisson Distribution. Scaling the constant Poisson rate from thirty years to ten gives mean and variance 2/3. The standard deviation is the square root of 2/3, approximately 0.816, so the answer is D.
Independent solution
Setup
Convert the stated long-window count rate into the requested time window.
Model
A Poisson count has variance equal to its mean.
Compute
Take the square root of the variance to obtain the standard deviation.
Answer
The requested standard deviation rounds to 0.816.
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
Priority alerts arrive at a server as a Poisson process with an average of 3.6 alerts per twelve-hour monitoring window. Calculate the standard deviation of the number of alerts during the next five hours.
The five-hour mean and variance are 3.6(5/12) = 1.5. The standard deviation is the square root of 1.5, approximately 1.225, so choice C.
Setup
Scale the twelve-hour rate to five hours.
Model
The five-hour alert count is Poisson, so its variance is also 1.5.
Compute
Take the square root of the five-hour variance.
Answer
The standard deviation rounds to 1.225.
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 Poisson 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.
