Exam P technique guide
Learn how to recognize the method, recall the formulas that control it, and work through 50 verification-gated sample-reference solutions.
Technique orientation
A uniform model assigns equal density across a continuous interval or equal mass across a finite set. That distinction matters: continuous probabilities are ratios of lengths, while discrete probabilities are ratios of counts. Start by writing the support and determine which version the problem uses.
Exam P combines uniform variables with conditioning, transformations, maxima and minima, and geometric regions. For one variable, the key is the overlap between the requested interval and the support. For joint uniform models, probability becomes an area or volume ratio only when the density is constant on the stated region.
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.
Continuous uniform density
Probability is the supported interval length multiplied by 1/(b − a).
Mean and variance
The variance depends on the width of the interval, not on its location.
Maximum of independent uniforms
All n observations must fall below x, which is where independence enters.
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.
1 verified reference
48 verified references
1 verified reference
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.
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.
46 verified problems
Discrete sums, continuous integrals, functions of loss, linearity, conditioning, and tail-based expectation.
