Start with the fundamentals of counting

Before diving into distributions, make sure you are completely comfortable with permutations, combinations, and the inclusion-exclusion principle. These concepts appear directly on the exam and also underpin many distribution problems.

Create a distribution reference sheet

Write out all the key distributions (Binomial, Poisson, Normal, Exponential, Gamma, Beta, Uniform) with their PDFs, CDFs, means, variances, and MGFs. Review this sheet daily until you can reproduce it from memory.

Drill conditional probability with tree diagrams

Many Exam P problems involve multi-step conditional reasoning. Drawing quick tree diagrams during the exam can prevent errors and save time compared to writing out formulas from scratch.

Master the double expectation theorem

E[X] = E[E[X|Y]] is one of the most powerful tools on this exam. Practice applying it to problems with mixed distributions and insurance scenarios involving random policy counts.

Practice with a strict 6-minute-per-question pace

The exam gives you 180 minutes for 30 questions. Train yourself to move on after 6 minutes even if you have not solved the problem. Flag it and return later.

Focus on transformations of random variables

Know how to find the distribution of Y = g(X) using the CDF method and the Jacobian method. These problems are common and mechanical once you have practiced the technique.

Use moment-generating functions strategically

MGFs uniquely determine distributions. If a problem asks you to identify a distribution from a sum of independent random variables, compute the MGF of the sum and match it to a known distribution.

Memorize key insurance formulas

Know the formulas for expected insurance payments with deductibles, limits, and coinsurance. The limited expected value E[X ^ d] = integral from 0 to d of S(x) dx is especially useful.

Simulate exam conditions at least three times

Take three full-length practice exams under timed conditions with no breaks. This builds the mental stamina needed for the actual 3-hour sitting.

Review wrong answers with a correction log

After every practice set, write down each mistake with the correct approach. Review this log weekly. Patterns in your errors reveal which topics need more attention.

P Study Tips