Distributions On Exam P

The July 2026 syllabus explicitly names the core univariate distributions candidates should know: binomial, geometric, hypergeometric, negative binomial, Poisson, and uniform on the discrete side, plus beta, exponential, gamma, normal, and uniform on the continuous side.

For most candidates, the hard part is not memorizing the list. The hard part is recognizing which story the problem is telling and which shortcut or relationship makes the arithmetic manageable.

Binomial means a fixed number of trials with success or failure on each one. Geometric and negative binomial are waiting-for-success stories. Hypergeometric is sampling without replacement. Poisson is event counts over exposure. Exponential is waiting time to the next Poisson event. Gamma extends that waiting-time idea to multiple events. Normal is the approximation and aggregation workhorse.

That map matters more than memorizing isolated formulas because Exam P often hides the distribution behind a story rather than naming it directly.

Know how to move between Poisson counts and exponential waiting times. Know when sampling is without replacement so hypergeometric, not binomial, is the right model. Know when normal approximation is reasonable and when continuity correction helps.

Also know the core moment patterns: binomial mean np and variance np(1-p), Poisson mean and variance both lambda, exponential mean 1/lambda, and the normal standardization step that turns a raw value into a z-score.

The most common mistake is choosing the model from surface wording instead of structure. 'Success' language does not automatically mean binomial. If the number of trials is random, or sampling is without replacement, or the question is really about waiting time, the right model changes.

The second common mistake is treating formulas as if they live alone. Exam P rewards seeing that distributions connect: Poisson to exponential, sums to normal approximation, and payment transformations back to expected value and variance.

A practical sequence is Poisson and exponential first because they connect directly. Then revisit normal because it becomes the approximation tool that cleans up many multistep problems. After that, fill in binomial-family distinctions and gamma as needed.