Exam P technique guide
Learn how to recognize the method, recall the formulas that control it, and work through 83 verification-gated sample-reference solutions.
Technique orientation
The exponential model is a one-parameter waiting-time distribution with a constant hazard rate. Before calculating, determine whether the supplied parameter is a rate or a mean and whether the event is a survival probability, an interval, a conditional residual lifetime, or a transformed payment.
Exam P often embeds exponential lifetimes in deductibles, minima, competing clocks, and conditional survival questions. The quickest reliable approach is to write the survival function first, translate every time into the parameter’s unit, and invoke memorylessness only when the condition is precisely survival beyond an elapsed time.
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.
Density and survival
If the mean is supplied, convert it first with λ = 1/E[X].
Memoryless property
The elapsed time disappears only after conditioning on survival, not after an arbitrary event.
Moments
Rate and scale conventions are reciprocals, a frequent source of wrong-answer choices.
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.
3 verified references
73 verified references
7 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.
71 verified problems
Count probabilities, rate scaling, aggregation, thinning, and links between Poisson counts and waiting times.
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.
