1. Probability Space. 1.1. The Axioms of Probability. 1.2. Conditional Probabilities and Bayes' Formula. 1.3. Independent Events. 1.4. Three or More Events -- 2. Random Variables. 2.1. Discrete Random Variables. 2.2. Continuous Random Variables. 2.3. Expectation. 2.4. Variance. 2.5. Normal Random Variables -- 3. Binomial and Poisson Random Variables. 3.1. Counting Principles. 3.2. Binomial Random Variables. 3.3. Poisson Random Variables -- 4. Limit Theorems. 4.1. The Law of Large Numbers. 4.2. Central Limit Theorem -- 5. Estimation and Hypothesis Testing. 5.1. Large Sample Estimation. 5.2. Hypothesis Testing. 5.3. Small Samples. 5.4. Chi-Square Tests -- 6. Linear Regression. 6.1. Fitting a Line to Data. 6.2. Inference for Regression -- 7. Moment Generating Functions and Sums of Independent Random Variables. 7.1. Moment Generating Functions. 7.2. Sums of Independent Random Variables -- 8. Transformations of Random Variables and Random Vectors. 8.1. Distribution Functions and Transformations of Random Variables. 8.2. Random Vectors. 8.3. Chi-square, Student Distributions and Normal Vectors