Exam P: Probability Study Guide
Probability theory, random variables, distributions, expected values, and insurance applications of probability.
Overview
Exam P tests your understanding of probability tools essential to actuarial science. It covers general probability, univariate and multivariate distributions, expected values, and the application of probability concepts to insurance and risk management problems. This is typically the first exam candidates attempt and serves as the foundation for all subsequent actuarial work.
Exam Format
- Duration
- 180 minutes (3 hours)
- Questions
- 30 multiple-choice questions
- Pathway
- SOA and CAS
- Format
- Computer-based testing (CBT)
Topic Breakdown
General Probability
10-15%Set functions, combinatorics, conditional probability, independence, Bayes theorem
Univariate Random Variables
30-40%PDFs, CDFs, moments, MGFs, common distributions (Binomial, Poisson, Normal, Exponential, Gamma, Beta, Uniform)
Multivariate Random Variables
30-40%Joint, marginal, and conditional distributions, covariance, correlation, bivariate Normal, order statistics
Risk Management Applications
15-20%Deductibles, policy limits, loss elimination ratios, stop-loss insurance, coinsurance
Recommended Study Approach
- 1
Build a strong foundation in set theory and counting principles before tackling distributions.
- 2
Master the core continuous distributions (Normal, Exponential, Gamma, Beta, Uniform) and their moment-generating functions.
- 3
Practice transforming random variables and computing conditional expectations extensively.
- 4
Focus on insurance-related problems involving deductibles, policy limits, and loss elimination ratios.
- 5
Work through at least 400 practice problems, as many past SOA sample questions reappear in modified form.
- 6
Use the memoryless property of the Exponential distribution as a time-saving shortcut on timed problems.