103 worked solutions
Exam P Conditional Probability problems
Conditioning, total probability, and Bayes calculations organized around the denominator that defines the updated sample space.
Exam P topic · 23–30% syllabus weight
Independently written solutions mapped to this official syllabus topic. Pages appear only after all required checks agree.
Topic orientation
Multivariate Random Variables studies joint, marginal, and conditional distributions together with covariance, correlation, and sums of random variables. The central question is how dependence changes a calculation that would otherwise look one-dimensional.
Problems commonly ask for a marginal or conditional quantity, a moment of a linear combination, or a distribution obtained from several components. A reliable setup identifies the joint support and preserves covariance terms until independence is justified.
Typical failure modes
Published ledger
Each entry shows its independent calculation record and links to the official source without reproducing protected wording.
Drill one method at a time
Each guide collects the questions above that turn on the same method, with the formulas and the errors that cost marks.
103 worked solutions
Conditioning, total probability, and Bayes calculations organized around the denominator that defines the updated sample space.
83 worked solutions
Waiting-time probabilities, parameter conversions, memorylessness, moments, and insurance-payment applications.
71 worked solutions
Count probabilities, rate scaling, aggregation, thinning, and links between Poisson counts and waiting times.
62 worked solutions
Standardization, inverse percentiles, linear combinations, normal approximations, and tail control.
57 worked solutions
Second moments, transformations, sums, covariance terms, and conditional variance decompositions.
55 worked solutions
Event independence, factorization, independent trials, and the consequences independence does—and does not—justify.
50 worked solutions
Continuous and discrete uniform models, interval geometry, transformations, order statistics, and moments.
46 worked solutions
Discrete sums, continuous integrals, functions of loss, linearity, conditioning, and tail-based expectation.
Study the whole topic offline
The 139 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.