Exam P topic · 44–50% syllabus weight

Univariate Random Variables

Independently written solutions mapped to this official syllabus topic. Pages appear only after all required checks agree.

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

Verified solutions

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