1. Introduction to Probability
The History of Probability
Interpretations of Probability
Experiments and Events
Set Theory
The Definition of Probability
Finite Sample Spaces
Counting Methods
Combinatorial Methods
Multinomial Coefficients
The Probability of a Union of Events
Statistical Swindles

2. Conditional Probability
The Definition of Conditional Probability
Independent Events
Bayes' Theorem
Markov Chains
The Gambler's Ruin Problem
3. Random Variables and Distribution
Random Variables and Discrete Distributions
Continuous Distributions
The Distribution Function
Bivariate Distributions
Marginal Distributions
Conditional Distributions
Multivariate Distributions
Functions of a Random Variable
Functions of Two or More Random Variables

4. Expectation
The Expectation of a Random Variable
Properties of Expectations
Variance
Moments
The Mean and The Median
Covariance and Correlation
Conditional Expectation
The Sample Mean
Utility

5. Special Distributions
Introduction
The Bernoulli and Binomial Distributions
The Hypergeometric Distribution
The Poisson Distribution
The Negative Binomial Distribution
The Normal Distribution
The Central Limit Theorem
The Correction for Continuity
The Gamma Distribution
The Beta Distribution
The Multinomial Distribution
The Bivariate Normal Distribution

6. Estimation
Statistical Inference
Prior and Posterior Distributions
Conjugate Prior Distributions
Bayes Estimators
Maximum Likelihood Estimators
Properties of Maximum Likelihood Estimators
Sufficient Statistics
Jointly Sufficient Statistics
Improving an Estimator

7. Sampling Distributions of Estimators
The Sampling Distribution of a Statistic
The Chi-Square Distribution
Joint Distribution of the Sample Mean and Sample Variance
The t Distribution
Confidence Intervals
Bayesian Analysis of Samples from a Normal Distribution
Unbiased Estimators
Fisher Information

9. Categorical Data and Nonparametric Methods
Tests of Goodness-of-Fit
Goodness-of-Fit for Composite Hypotheses
Conngency Tables
Tests of Homogeneit
Simpson's Paradox
Kolmogorov-Smirnov Test
Robust Estimation
Sign and Rank Tests

10. Linear Statistical Models
The Method of Least Squares
Regression
Statistical Inference in Simple Linear Regression
Bayesian Inference in Simple Linear Regression
The General Linear Model and Multiple Regression
Analysis of Variance
The Two-Way Layout
The Two-Way Layout with Replications

11. Simulation
Why is Simulation Useful?
Simulating Specific Distributions
Importance Sampling
Markov Chain Monte Carlo
The Bootstrap