SOA Exam P: Probability (Part 1 of 2) [Actuarial]

Master the foundations of set theory for probability, including sample spaces and events. Learn about universal sets, elements, and subsets, plus set operations (union, intersection, complement, difference) with Venn diagrams.

Explore conditional probability and independence, with formal definitions, tree diagrams, and practical examples from card draws, Bayesian probability, Monty Hall, and real-world risks.

Learn Bayes theorem and credibility in probability, illustrated with conditional probability using a deck-of-cards tree diagram and a two-risk driver example for insurance.

Work through general probability tutorials built from sample exam questions, focusing on set theory, independence, Bayes' theorem, conditional probability, and problem-solving with Venn diagrams for self evaluation.

Explore discrete random variables, their probability distributions and the cumulative distribution function, with examples including binomial, hypergeometric, geometric, and discrete uniform cases.

Explore measures of central tendency, including mean (expected value), median, mode, and mid range, with practical examples and linear transformations, plus an introduction to percentiles and quartiles.

Learn measures of dispersion: min, max, range, interquartile range, variance, standard deviation; understand their link to the mean via the second moment, and use z-scores for cross-distribution comparison.

Explore Chebyshev's theorem, the Markov inequality, coefficient of variation, and conditional expectation and variance with practical proofs and examples.

This lecture introduces jointly distributed discrete random variables and their probability generating function, illustrating independence versus dependence with birth examples, and explaining moments and variance relationships.

Explore discrete random variables through practical tutorial questions on probability distributions, expectation and variance, conditional and joint distributions, and deductible concepts for actuarial exam prep.

Explore discrete uniform, Bernoulli, binomial, and geometric distributions, learn to identify them from problem descriptions, and apply their mean and variance formulas.

Examine the negative binomial distribution as a sum of geometric trials and the hypergeometric distribution for sampling without replacement. Learn their mean and variance and solve real-world problems.

Explore the Poisson distribution, its probability function, and Poisson process, modeling sporadic events like misprints, calls, and car accidents, with scalability, sums of Poisson variables, and the mean equals lambda.

Explore discrete distributions through a high-difficulty tutorial solving exam questions on binomial, multinomial, hypergeometric, trinomial, negative binomial, and Poisson models, with conditional probabilities and independence in actuarial contexts.

Explore continuous distributions by defining and differentiating cumulative distribution functions and density functions. Apply integration to relate the cdf to the pdf and compute probabilities.

Explore how to compute expected values, variances, modes, medians, and percentiles for continuous distributions using density and CDF methods, including transforming variables and deriving expected values from the survivorship function.

Explore mixed distributions, including two-point mixtures of continuous and discrete components, and apply deductibles and caps to insurance loss modeling, with moment calculations.

Explore caps and deductibles using the cdf method to simplify expectations; learn moment generating functions for discrete and continuous distributions and derive moments quickly.

Explore techniques for continuous distributions through practice problems on CDFs, conditional probability, proportional densities, deductibles and benefit limits, percentiles, moment generating functions, and mode in mixed distributions.