Copies of the classnotes are on the internet in PDF format as given below. The notes and supplements may contain hyperlinks to posted webpages; the links appear in red fonts. The "Proofs of Theorems" files were prepared in Beamer. The "Printout of Proofs" are printable PDF files of the Beamer slides without the pauses. These notes have not been classroom tested and may have typographical errors.

The catalog description of Foundations of Probability and Statistics–Calculus Based (MATH 2050) is: "A calculus-based introduction to probability and statistical inference. Basic probability concepts, mathematical expectation, discrete and continuous probability distributions, sampling distributions, one and two-sample estimation, and hypothesis testing techniques will be developed and used; linear regression and correlation." The formal prerequisite is Calculus 1 (MATH 1910). The catalog description for Mathematical Statistics 1 (Stat 4047/5047) is: "An introduction to the theory of probability and mathematical statistics. Topics will include discrete and continuous probability distributions and their applications, mathematical expectation and moment generating functions, functions of random variables and transformations, sampling distributions, the central limit theorem, χ-square, t and F distributions." The prerequisites are Linear Algebra (MATH 2010), Foundations of Probability and Statistics–Calculus Based (MATH 2050), and Calculus 3 (MATH 2110). These descriptions are based on the ETSU 2019-20 Undergraduate Catalog.

In these notes, we concentrate on the mathematical theory of probability. The material presented here is more advanced than that of Foundations of Probability and Statistics–Calculus Based, and less advanced than that of Mathematical Statistics 1 (STAT 4047/5047). So this material is appropriate for an "intermediate" probability and statistics class, though such a class does not exist at ETSU. As the publisher's webpage for the text book says, the book "was written for a one- or two-semester probability and statistics course. This course is offered primarily at four-year institutions and taken mostly by sophomore and junior level students majoring in mathematics or statistics. Calculus is a prerequisite, and a familiarity with the concepts and elementary properties of vectors and matrices is a plus."

Preface. PDF.

1. Introduction to Probability.

• 1.1. The History of Probability. Section 1.1 notes
• 1.2. Interpretations of Probability. Section 1.2 notes
• 1.3. Experiments and Events. Section 1.3 notes
• 1.4. Set Theory. Section 1.4 notes
• 1.5. The Definition of Probability. Section 1.5 notes
• Supplement. Proofs of Theorems from Section 1.5. Beamer file of Section 1.5 proofs
• Supplement. Printouts of Proofs from Section 1.5. Print file of Section 1.5 proofs
• 1.6. Finite Sample Spaces. Section 1.6 notes
• 1.7. Counting Methods. Section 1.7 notes (Contains the Birthday Problem.)
• 1.8. Combinatorial Methods. Section 1.8 notes (Contains the Tennis Tournament Problem.)
• 1.9. Multinomial Coefficients. Section 1.9 notes
• 1.10. The Probability of a Union of Events. Section 1.10 notes (Contains the Matching Problem.)
• Supplement. Proofs of Theorems from Section 1.10. Beamer file of Section 1.10 proofs
• Supplement. Printouts of Proofs from Section 1.10. Print file of Section 1.10 proofs
• 1.11. Statistical Swindles. Section 1.11 notes
• Study Guide 1

2. Conditional Probability.

• 2.1. The Definition of Conditional Probability. Section 2.1 notes (Contains a description of the game of craps.)
• Supplement. Proofs of Theorems from Section 2.1. Beamer file of Section 2.1 proofs
• Supplement. Printouts of Proofs from Section 2.1. Print file of Section 2.1 proofs
• 2.2. Independent Events. Section 2.2 notes (Contains the Collector's Problem.)
• Supplement. Proofs of Theorems from Section 2.2. Beamer file of Section 2.2 proofs
• Supplement. Printouts of Proofs from Section 2.2. Print file of Section 2.2 proofs
• 2.3. Bayes' Theorem. Section 2.3 notes
• 2.4. The Gambler's Ruin Problem.
• Study Guide 2.

3. Random Variables and Distributions.

• 3.1. Random Variables and Discrete Distributions.
• 3.2. Continuous Distributions.
• 3.3. The Cumulative Distribution Function.
• 3.4. Bivariate Distributions.
• 3.5. Marginal Distributions.
• 3.6. Conditional Distributions.
• 3.7. Multivariate Distributions.
• 3.8. Functions of a Random Variable.
• 3.9. Functions of Two or More Random Variables.
• 3.10. Markov Chains.
• Study Guide 3.

4. Expectation.

• 4.1. The Expectation of a Random Variable.
• 4.2. Properties of Expectations.
• 4.3. Variance.
• 4.4. Moments.
• 4.5. The Mean and the Median.
• 4.6. Covariance and Correlation.
• 4.7. Conditional Expectation.
• 4.8. Utility.
• Study Guide 4.

5. Special Distributions.

• 5.1. Introduction.
• 5.2. The Bernoulli and Binomial Distributions.
• 5.3. The Hypergeometric Distribution.
• 5.4. The Poisson Distributions.
• 5.5. The Negative Binomial Distributions.
• 5.6. The Normal Distributions.
• 5.7. The Gamma Distributions.
• 5.8. The Beta Distributions.
• 5.9. The Multinomial Distributions.
• 5.10. The Bivariate Normal Distributions.
• Study Guide 5.

6. Large Random Samples.

• 6.1. Introduction.
• 6.2. The Law of Large Numbers.
• 6.3. The Central limit Theorem.
• 6.4. The Correction for Continuity.
• Study Guide 6.

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