Probability Fundamentals
- Set Functions, Sample Spaces, and Axioms of Probability (25 min)
- Combinations and Permutations (17 min)
- Independence and Probabilities of Independent Events (30 min)
- Mutually Exclusive Events (14 min)
- Addition and Multiplication Rules (14 min)
- Permutations, Ordered Counting, and the Multiplication Principle (23 min)
Conditional Probability & Bayes
- Conditional Probability (23 min)
- Bayes' Theorem and Law of Total Probability (23 min)
- Bayesian Odds, Likelihood Ratios, and Base-Rate Traps (16 min)
Continuous Distributions
- Probability, Random Variables, PDFs, and CDFs (18 min)
- Conditional Probabilities for Random Variables (17 min)
- Common Parametric Distributions (18 min)
- The Gamma Distribution and the Poisson Connection (11 min)
- The Beta Distribution (11 min)
Expectation & Variance
- Expected Values: Moments, Mode, Median, and Percentiles (21 min)
- Variance, Standard Deviation, and Coefficient of Variation (19 min)
- Moment Generating Functions (12 min)
Insurance Applications
- Insurance Payments: Deductibles, Coinsurance, Benefit Limits, and Inflation (26 min)
- Moments of Loss and Payment Random Variables (23 min)
Discrete Distributions
- Discrete Counting Distributions: Binomial, Negative Binomial, Hypergeometric (14 min)
- Waiting-Time Distributions: Geometric and Poisson (14 min)
- Discrete Uniform Random Variables (10 min)
Joint & Marginal Distributions
- Joint Probability Functions and Joint CDFs for Discrete Random Variables (20 min)
- Conditional and Marginal Probability Functions for Discrete Random Variables (18 min)
- Moments for Joint, Conditional, and Marginal Discrete Distributions (23 min)
- Variance and Standard Deviation for Conditional and Marginal Distributions (18 min)
- Covariance and Correlation Coefficient for Discrete Random Variables (15 min)
- Joint Distribution of Order Statistics (19 min)
- Linear Combinations of Independent Discrete and Normal Random Variables (16 min)
- Moments for Linear Combinations of Independent Random Variables (23 min)
- Central Limit Theorem: Approximations for Linear Combinations of iid Random Variables (22 min)
