Exam P technique guide
Learn how to recognize the method, recall the formulas that control it, and work through 71 verification-gated sample-reference solutions.
Technique orientation
A Poisson variable counts events in a fixed exposure when events occur independently at a stable average rate. The parameter is the expected count for the exact interval or exposure under study, so the first calculation should rescale the rate before any probability mass is evaluated.
Exam P tests exact counts, tails, combined independent sources, conditional allocation of a total, and compound-count moments. A useful solution states the exposure-specific mean, decides whether the event is exact or cumulative, and keeps enough precision for the final answer-choice comparison.
Recognition audit
Before calculation
Name the requested quantity, mark its units or time point, and identify the assumption that permits the formula. Only then insert the numerical inputs. This separates model errors from arithmetic errors and makes the answer-choice comparison auditable.
Formula core
These identities are starting points, not substitutes for checking support, timing, rate periods, or independence assumptions.
Poisson probability mass
Here μ is the expected count over the full exposure used in the question.
Mean and variance
The equality of mean and variance is also a quick diagnostic for the parameterization.
Independent aggregation
Add parameters only when the component counts are independent.
Three failure modes to catch
Verified practice ledger
The list is grouped by current official syllabus area. Every link opens a step-labeled solution, verification artifact, distractor analysis, and one fully worked original variant.
5 verified references
55 verified references
11 verified references
Continue the study loop
The complete Exam P manual includes all active sample-reference solutions, their wrong-choice analysis, and one independently written worked variant per reference. The free formula sheet is the compact companion for recall between practice sessions.
Related drills
Switch techniques when you can identify the current method before writing a formula and can explain each wrong-choice mechanism.
103 verified problems
Conditioning, total probability, and Bayes calculations organized around the denominator that defines the updated sample space.
83 verified problems
Waiting-time probabilities, parameter conversions, memorylessness, moments, and insurance-payment applications.
62 verified problems
Standardization, inverse percentiles, linear combinations, normal approximations, and tail control.
57 verified problems
Second moments, transformations, sums, covariance terms, and conditional variance decompositions.
55 verified problems
Event independence, factorization, independent trials, and the consequences independence does—and does not—justify.
50 verified problems
Continuous and discrete uniform models, interval geometry, transformations, order statistics, and moments.
46 verified problems
Discrete sums, continuous integrals, functions of loss, linearity, conditioning, and tail-based expectation.
