Worked solution · Exam P
This Exam P sample reference tests Poisson Distribution. Independence lets the monthly Poisson variances add across two locations and three months. The total variance is three times the combined monthly mean, or 135, so the answer is B.
Independent solution
Setup
Represent each location-month count separately. Every component is Poisson, so its variance equals its mean.
Model
The six counts are mutually independent, so the variance of their sum is the sum of their variances.
Compute
Each month contributes variance 45, and there are three independent months.
Answer
The variance of the full three-month total is 135.
Test the method on unseen problems
30 original multivariate 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 greenhouse uses three independent sensor sectors. In a week, the numbers of unusual detections in the sectors are independent Poisson random variables with means 1.5, 2.5, and 4.0. Counts are also independent from week to week. Calculate the variance of the total number of detections over five weeks.
The three sectors contribute a combined weekly variance of 8. Across five independent weeks the total variance is 40, which is choice C.
Setup
For each sector and week, the Poisson variance equals the corresponding sector mean.
Model
Add the independent sector variances within a week, then add the five independent weekly totals.
Compute
Five weekly totals each contribute variance 8.
Answer
The five-week total has variance 40.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 140 Exam P multivariate 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.
