Exam P topic · 44–50% syllabus weight

How to study Exam P’s 44–50% univariate area

Diagnose six separate jobs, use a 12-session audit, then practise them across 387 independently written solutions. The published weight sets relative emphasis; it does not guarantee a fixed question count.

Six-block diagnostic

Make the largest syllabus area smaller

The official syllabus names models, distribution functions, moments, transformations, and insurance payments. The blocks below are an ActuaryProof study framework for locating the decision that failed.

Actual page of original Exam P univariate practice questions from the ActuaryProof workbook — Actual independently produced question page from workbook version 1.0.0, updated 2026-08-24. It shows independently written practice output. The official syllabus, not this image, supports the 44–50% weight; the six-block audit is an editorial recommendation.

Block	Question before calculating	Typical failure
Model	Which distribution or definition fits, and why?	Choosing from a keyword without checking assumptions
Support	Which values of the variable are possible?	Summing or integrating outside the support
Tail or CDF	Which event is requested?	Using a lower tail for an upper-tail event
Moments	Which variable has the requested mean or variance?	Applying a formula to the wrong transformed variable
Transformation	How do intervals, support points, or atoms move?	Transforming values without moving their probabilities
Insurance payment	What do the deductible, limit, and coinsurance do to payment?	Solving for loss when the question asks for insurer payment

12-session audit

Use two attempts per block

In the first session, work with notes and record the setup. In the second, close the notes, change a parameter or boundary, and rebuild the solution. A correct answer does not close a block unless you can state the support, justify the model, and perform one independent check.

Block	First-pass error	Changed input	Independent check	Closed?
Tail or CDF	Computed F(x) instead of 1 − F(x)	Changed the threshold	Complement agrees	Yes
Insurance payment	Ignored the policy limit	Lowered the limit	Payment never exceeds the limit	No

The free pages below are enough to begin the audit. For a concentrated second pass, the30-problem univariate workbook contains original practice, wrong-choice analysis, and independent checks. It cannot forecast an exam form or guarantee an outcome.

Topic orientation

What this topic tests

Univariate Random Variables covers discrete and continuous distributions, density and distribution functions, moments, transformations, insurance payment variables, and percentiles. It is the largest Probability syllabus area and rewards quick recognition of a model’s defining identities.

The exam tests whether a candidate can respect support, normalize a model, choose the correct tail, and connect distribution parameters to the requested quantity. The pages below show those decisions before the arithmetic.

Typical failure modes

Integrating or summing outside the variable’s support
Confusing a density value with a probability
Using the wrong tail or failing to invert a CDF correctly

Published ledger

Exam P Univariate Random Variables practice problems and solutions

Each entry shows its independent calculation record and links to the official source without reproducing protected wording.

Drill one method at a time

Techniques that keep appearing in Univariate Random Variables

Each guide collects the questions above that turn on the same method, with the formulas and the errors that cost marks.

103 worked solutions

Exam P Conditional Probability problems

Conditioning, total probability, and Bayes calculations organized around the denominator that defines the updated sample space.

83 worked solutions

Exam P Exponential Distribution problems

Waiting-time probabilities, parameter conversions, memorylessness, moments, and insurance-payment applications.

72 worked solutions

Exam P Poisson Distribution problems

Count probabilities, rate scaling, aggregation, thinning, and links between Poisson counts and waiting times.

62 worked solutions

Exam P Normal Distribution problems

Standardization, inverse percentiles, linear combinations, normal approximations, and tail control.

57 worked solutions

Exam P Variance problems

Second moments, transformations, sums, covariance terms, and conditional variance decompositions.

55 worked solutions

Exam P Independence problems

Event independence, factorization, independent trials, and the consequences independence does—and does not—justify.

50 worked solutions

Exam P Uniform Distribution problems

Continuous and discrete uniform models, interval geometry, transformations, order statistics, and moments.

46 worked solutions

Exam P Tail Integral Formula and Expected Value problems

Tail-integral proof, survival-function expectation, discrete tail sums, loss payments, linearity, and conditioning.

Study the whole topic offline

Every Exam P sample question in one searchable PDF

The 387 pages above stay free. The manual collects the complete Exam P sample set in syllabus order, with the same working, the wrong-choice notes, and one new practice problem per question.

See the Exam P study manual PDF — $49 Free Exam P formula sheet All Exam P sample-question solutions

Sources and accountability

Primary sources and correction path

September 2026 SOA Exam P syllabusAuthority for the 44–50% weight and the univariate learning outcomes.

ActuaryProof publishes the independent explanations on this page. Official exam facts on this page come from the sources above; schedules, study ledgers, and checking protocols are ActuaryProof editorial tools unless stated otherwise. Read about the publisher or report a suspected error.

Primary sources last checked: August 31, 2026.