Index of PDF Files

This index contains a list of all PDF files for the sections of expository text. If you are using the Firefox browser, please go the main home page of the project, where you can access not only the expository text, but applets, biographical skectches, data sets, and other interactive features.

Project Information

• Introduction
• Credits

Expository Material

0. Foundations
   • Sets
   • Functions
   • Relations
   • Partial Orders
   • Equivalence Relations
   • Cardinality
   • Counting Measure
   • Combinatorial Structures
   • Measure Theory
   • Answers to Selected Exercises
1. Probability Spaces
   • Random Experiments
   • Events and Random Variables
   • Probability Measures
   • Conditional Probability
   • Independence
   • Convergence
   • Measure Theory
   • Answers to selected exercises
2. Distributions
   • Discrete Distributions
   • Continuous Distributions
   • Mixed Distributions
   • Joint Distributions
   • Conditional Distributions
   • Distribution and Quantile Functions
   • Transformations of Variables
   • Convergence in Distribution
   • Answers to selected exercises
3. Expected Value
   • Definitions and Properties
   • Variance and Higher Moments
   • Covariance and Correlation
   • Generating Functions
   • Conditional Expected Value
   • Expected Value and Covariance Matrices
   • Answers to Selected Exercises
4. Special Distributions
   • Introduction
   • The Normal Distribution
   • The Gamma Distribution
   • The Chi-Square Distribution
   • The Student t Distribution
   • The F Distribution
   • The Multivariate Normal Distribution
   • The Beta Distribution
   • The Weibull Distribution
   • The Zeta Distribution
   • The Pareto Distribution
   • The Logistic Distribution
   • The Lognormal Distribution
   • The Extreme Value Distribution
   • Benford's Law
   • Answers to Selected Exercises
5. Random Samples
   • Introduction
   • The Sample Mean and the Law of Large Numbers
   • The Sample Variance
   • Partial Sums and the Central Limit Theorem
   • Special Properties of Normal Samples
   • Order Statistics
   • Sample Covariance and Correlation
   • Answers to Selected Exercises
6. Point Estimation
   • Estimators
   • The Method of Moments
   • Maximum Likelihood
   • Bayes Estimators
   • Best Unbiased Estimators
   • Sufficient, Complete and Ancillary Statistics
7. Set Estimation
   • Introduction
   • Estimation the Normal Model
   • Estimation in the Bernoulli Model
   • Estimation in the Two-Sample Normal Model
   • Bayesian Set Estimation
   • Answers to Selected Exercises
8. Hypothesis Testing
   • Introduction
   • Tests in the Normal Model
   • Tests in the Bernoulli Model
   • Tests in the Two-Sample Normal Model
   • Likelihood Ratio Tests
   • Chi-Square Tests
   • Probability Plots
   • Answers to Selected Exercises
9. Geometric Models
   • Buffon's Problems
   • Bertrand's Paradox
   • Random Triangles
   • Answers to Selected Exercises
10. Bernoulli Trials
    • Introduction
    • The Binomial Distribution
    • The Geometric Distribution
    • The Negative Binomial Distribution
    • The Multinomial Distribution
    • The Simple Random Walk
    • Answers to Selected Exercises
11. Finite Sampling Models
    • Introduction
    • The Hypergeometric Distribution
    • The Multivariate Hypergeometric Distribution
    • Order Statistics
    • The Matching Problem
    • The Birthday Problem
    • The Coupon Collector Problem
    • Pólya's Urn and the Beta-Bernoulli Process
    • The Secretary Problem
    • Answers to Selected Exercises
12. Games of Chance
    • Introduction
    • Poker
    • Simple Dice Games
    • Craps
    • Roulette
    • The Monty Hall Problem
    • Lotteries
    • Red and Black
    • Timid Play
    • Bold Play
    • Optimal Strategies
    • Answers to Selected Exercises
13. The Poisson Process
    • Introduction
    • The Exponential Distribution
    • The Gamma Distribution
    • The Poisson Distribution
    • Splitting a Poisson Process
    • Bernoulli Trials and the Poisson Process
    • Higher Dimensional Poisson Processes
    • Answers to Selected Exercise
14. Renewal Processes
    • Introduction
    • Renewal Equations
    • Renewal Limit Theorems
15. Markov Chains
    • Introduction
    • Recurrence and Transience
    • Periodicity
    • Invariant and Limiting Distributions
    • Time Reversal
    • The Ehrenfest Chains
    • The Bernoulli Laplace Chain
    • Reliability Chains
    • The Branching Chain
    • Queuing Chains
    • Birth Death Chains
    • Random Walks on Graphs
    • Answers to Selected Exercises
16. Interacting Particle Systems
    • The Fire Process
    • The Voter Process