Worked solution · Exam P
This Exam P sample reference tests Poisson Distribution. This is a Poisson upper-tail calculation with the parameter inferred from the standard deviation. A standard deviation of 2 means the Poisson mean is 4, so complementing the probabilities of zero and one call gives 0.9084 and choice E.
Independent solution
Setup
For a Poisson count, the variance equals the mean. Square the supplied standard deviation to obtain the parameter.
Model
Use the complement of the two excluded low-count outcomes.
Compute
Evaluate the first two Poisson probabilities.
Answer
The upper-tail probability rounds to 0.908.
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
The number of overnight incidents recorded by a monitoring service has a Poisson distribution with variance 3. Its dashboard adds one standing system check to the incident count. Calculate the probability that the displayed count is at most 2.
The Poisson variance gives a mean of 3. A display no greater than two permits at most one actual incident. Adding the zero- and one-incident probabilities gives 0.1991 and choice C.
Setup
Use the Poisson variance to identify its parameter.
Model
Translate the dashboard threshold back to the underlying incident count.
Compute
Add the two qualifying Poisson masses.
Answer
The dashboard is at most two with probability 0.1991.
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.
