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Prepare for the Society of Actuaries Exam P with this comprehensive 12-hour course covering probability theory fundamentals essential for aspiring actuaries. Master general probability concepts including basic probability rules, Venn diagrams, DeMorgan's laws, conditional probabilities, independent events, law of total probability, and Bayes' theorem through detailed explanations and practical examples. Explore counting methods such as permutations, combinations, and distinguishable permutations with replacement scenarios. Dive deep into univariate random variables, learning to work with both discrete and continuous cases, including functions, moments, expected values, variance, standard deviation, and coefficient of variation. Study commonly tested discrete distributions including binomial (Bernoulli), multinomial, hypergeometric, geometric (negative binomial), and Poisson distributions, as well as continuous distributions such as exponential (gamma), beta, normal, and lognormal distributions. Apply probability concepts to actuarial contexts through policy modifications, deductible examples with exponential and uniform losses, and snowstorm scenarios. Advance to multivariate random variables covering joint, marginal, and conditional distributions, expected values, law of total expectation and variance, discrete mixtures, covariance and correlation, and operations with minimums and maximums. Conclude with aggregate models and the central limit theorem for summing independent random variables, providing a complete foundation for SOA Exam P success under the guidance of Professor Stephen Paris, PhD, ASA.
