Mathematical Statistics I
Mathematical Statistics I
STAT-2311, Fall 2026. The course builds, from the axioms upward, the probabilistic foundation on which statistical inference in economics and finance rests: descriptive measures, probability and counting, conditional probability and Bayes' rule, discrete and continuous random variables, and finally several random variables at once — joint and conditional distributions, independence, covariance, and the arithmetic of linear combinations.
On this page
Course information
Sections and times
| Section | Wednesday | Saturday |
|---|---|---|
| 10462 | 10:00-11:15, D109 | 10:00-11:15, D109 |
| 10463 | 11:30-12:45, A210 | 11:30-12:45, B202 |
| 10464 | 13:00-14:15, A110 | 13:00-14:15, B202 |
Learning outcomes
How the course runs
The course meets twice a week for 75 minutes, on Wednesdays and Saturdays. Each session pairs a lecture that develops the theory with worked problems solved at the board. Derivations are done in full, and students are expected to reproduce them; roughly a third of each session is given over to guided problem solving.
Between sessions students work through biweekly problem sets on WeBWorK. The problems are randomised, so each student receives a different version and gets immediate feedback. Alongside the lectures, the teaching assistant runs seven biweekly tutorials — one in each week that a problem set closes — as working sessions rather than repeat lectures.
Assessment is delivered on the same platform as the practice, so the tool used for homework is the tool used for examination and no student meets the interface for the first time under exam conditions. Every probability model introduced in the course is motivated by an economic or financial application: insurance claims, default counts, waiting times, portfolio variance.
Assessment
Problem sets
10% Seven, biweeklyQuiz I
10% 14 October · Chapters 1-2Midterm Examination I
30% 24 October · Chapters 1-3 (3.1-3.8)Quiz II
10% 12 December · Chapter 4, 5.1-5.8Midterm Examination II
40% 19 December · ComprehensiveEvery quiz and examination is written on WeBWorK during the regular class period of each section, on a laptop. Statistical tables and a formula sheet are built into each set. Problems are set in several parts and credit is awarded part by part, so intermediate quantities carry marks of their own.
Problem set deadlines
Seven sets are released on WeBWorK at two-week intervals and close at 23:59 on the dates below. Attempts before the deadline are unlimited, and the lowest set is dropped. A TA-led tutorial runs in each of these weeks, before the deadline.
| Set | Closes | Covers |
|---|---|---|
| 1 | 26 September 2026 | Chapter 1 and 2.1-2.8 |
| 2 | 10 October 2026 | 2.9-2.12 and 3.1-3.3 |
| 3 | 21 October 2026 | 3.4-3.8 |
| 4 | 7 November 2026 | 3.9-3.11 and 4.1-4.4 |
| 5 | 21 November 2026 | 4.5-4.11 |
| 6 | 5 December 2026 | 5.1-5.6 |
| 7 | 16 December 2026 | 5.7-5.12 |
Course plan
| Date | Topic | Reading and preparation |
|---|---|---|
| 9 September | Course orientation. What statistics is: populations, samples, and the inferential problem. Describing a data set: frequency distributions and relative frequency histograms. | Wackerly, Mathematical Statistics with Applications, 7th ed., §§1.1–1.3. Skim the Chapter 1 introduction before class. |
| 12 September | Numerical descriptive measures: the mean, the variance and the standard deviation. Tchebysheff's theorem and the empirical rule as distribution-free bounds. Why inference requires a measure of goodness. | Wackerly §§1.4–1.6. Exercises at the end of §§1.3–1.5. |
| 16 September | The probability of an event: sample spaces, simple and compound events, set notation, and the three axioms. The sample-point method for discrete sample spaces. | Wackerly §§2.1–2.5. Exercises at the end of §2.4. |
| 19 September | Tools for counting sample points: the mn rule, permutations, combinations, and partitions into groups. Sampling with and without replacement. | Wackerly §2.6. Exercises at the end of §2.6. |
| 23 September | Conditional probability and the independence of events; independence contrasted with mutual exclusivity. | Wackerly §2.7. Exercises at the end of §2.7. |
| 26 September | The additive and multiplicative laws of probability. Probabilities of unions, intersections and complements. | Wackerly §2.8. Exercises at the end of §2.8. Problem Set 1 due at 23:59. Tutorial week: TA-led tutorial before the deadline. |
| 30 September | Calculating the probability of an event: the event-composition method. Extended worked problems on system reliability and compound financial events. | Wackerly §2.9. Exercises at the end of §2.9. |
| 3 October | The law of total probability and Bayes' rule. Applications: credit screening, diagnostic testing, and the revision of prior beliefs in the light of evidence. | Wackerly §2.10. Exercises at the end of §2.10. |
| 7 October | Numerical events and random variables: the passage from events to distributions. Chapter 2 synthesis and problem clinic. | Wackerly §§2.11–2.12. Supplementary exercises, Chapter 2. |
| 10 October | Discrete random variables: the probability mass function and its properties. Expected value of a random variable and of a function of one; variance and standard deviation. | Wackerly §§3.1–3.3. Exercises at the end of §3.3. Problem Set 2 due at 23:59. Tutorial week: TA-led tutorial before the deadline. |
| 14 October | Quiz I on WeBWorK, first 30 minutes of class (Chapters 1–2). The binomial distribution: derivation from Bernoulli trials, mean, variance, and use in counting defaults and defects. | Prepare Wackerly Chapters 1–2 for the quiz. Reading for the lecture: §3.4. |
| 17 October | The geometric and negative binomial distributions: waiting for the first success and for the rth success; memorylessness in discrete time. | Wackerly §§3.5–3.6. Exercises at the end of §§3.5–3.6. |
| 21 October | The hypergeometric and Poisson distributions; the Poisson limit of the binomial. Review session for Midterm Examination I. | Wackerly §§3.7–3.8. Supplementary exercises, Chapters 1–3 (§§3.1–3.8). Problem Set 3 due at 23:59. Tutorial week: TA-led tutorial before the deadline. |
| 24 October | Midterm Examination I on WeBWorK — Chapters 1–3 (§§3.1–3.8), written during the regular class period of each section. | Wackerly Chapters 1–2 and §§3.1–3.8. Bring a charged laptop. Statistical tables and a formula sheet are built into the WeBWorK set. |
| 28 October | Moments and moment-generating functions of discrete random variables; recovering the moments of a distribution by differentiation. | Wackerly §3.9. Exercises at the end of §3.9. |
| 31 October | Probability-generating functions. Tchebysheff's theorem for discrete random variables. Chapter 3 synthesis: choosing among the discrete models. | Wackerly §§3.10–3.11. Supplementary exercises, Chapter 3. |
| 4 November | Continuous random variables: the distribution function and the density function; the probability of an interval as an area under the density. | Wackerly §§4.1–4.2. Exercises at the end of §4.2. |
| 7 November | Expected values for continuous random variables. The uniform distribution and its role as a reference model. | Wackerly §§4.3–4.4. Exercises at the end of §§4.3–4.4. Problem Set 4 due at 23:59. Tutorial week: TA-led tutorial before the deadline. |
| 11 November | The normal distribution: shape, standardisation, use of the normal tables, and its place in the modelling of asset returns. | Wackerly §4.5. Exercises at the end of §4.5. |
| 14 November | The gamma family: the gamma, exponential and chi-square distributions. Waiting times and lifetimes; the memoryless property in continuous time. | Wackerly §4.6. Exercises at the end of §4.6. |
| 18 November | The beta distribution as a model for proportions. Choosing among the continuous models: general comments and comparisons. | Wackerly §§4.7–4.8. Exercises at the end of §4.7. |
| 21 November | Moment-generating functions for continuous random variables; Tchebysheff's theorem; expectations of discontinuous functions. Chapter 4 synthesis. | Wackerly §§4.9–4.11. Supplementary exercises, Chapter 4. Problem Set 5 due at 23:59. Tutorial week: TA-led tutorial before the deadline. |
| 25 November | Multivariate probability distributions: joint distribution functions and joint densities for the discrete and the continuous case. | Wackerly §§5.1–5.2. Exercises at the end of §5.2. |
| 28 November | Marginal and conditional distributions: recovering one variable's behaviour from the joint law, and conditioning on the other. | Wackerly §5.3. Exercises at the end of §5.3. |
| 2 December | Independent random variables: the factorisation criterion, and the ways independence fails in economic data. | Wackerly §5.4. Exercises at the end of §5.4. |
| 5 December | The expected value of a function of several random variables. Covariance: definition, computation, and interpretation as co-movement. | Wackerly §§5.5–5.6. Exercises at the end of §§5.5–5.6. Problem Set 6 due at 23:59. Tutorial week: TA-led tutorial before the deadline. |
| 9 December | The mean and variance of a linear combination of random variables; the variance of a two-asset portfolio and the arithmetic of diversification. The multinomial distribution. | Wackerly §§5.7–5.8. Exercises at the end of §§5.7–5.8. |
| 12 December | Quiz II on WeBWorK, first 30 minutes of class (Chapter 4 and §§5.1–5.8). The bivariate normal distribution. | Prepare Wackerly Chapter 4 and §§5.1–5.8 for the quiz. Reading for the lecture: §5.9. |
| 16 December | Conditional expectations and the regression function. Chapter 5 synthesis and comprehensive review of Chapters 1–5 in preparation for Midterm Examination II. | Wackerly §§5.10–5.12. Supplementary exercises, Chapter 5. Problem Set 7 due at 23:59. Tutorial week: TA-led tutorial before the deadline. |
| 19 December | Midterm Examination II on WeBWorK — comprehensive over Chapters 1–5, with emphasis on Chapters 4–5, written during the regular class period of each section. | Wackerly Chapters 1–5, with emphasis on Chapters 4–5. Bring a charged laptop. Statistical tables and a formula sheet are built into the WeBWorK set. |
Reading
Required
Wackerly, D. D., Mendenhall, W. and Scheaffer, R. L. (2008). Mathematical Statistics with Applications, 7th edition. Brooks/Cole, Cengage Learning. The course follows Chapters 1 to 5 closely; the statistical tables in the appendix are the tables used in class.
Recommended
Casella, G. and Berger, R. L. (2002). Statistical Inference, 2nd edition, Chapters 1-4 — for students who want a more demanding treatment.
Ross, S. M. (2019). A First Course in Probability, 10th edition — a gentler source of worked examples on combinatorics and conditional probability.
Hogg, McKean and Craig (2019). Introduction to Mathematical Statistics, 8th edition — a second exposition of multivariate distributions.
Lecture slides, prepared in Quarto, are posted on Blackboard Learn after each session. They are a companion to the text, not a substitute for it.
Practical matters
Blackboard Learn
The single point of distribution for the course: slides after each session, problem set announcements and deadlines, and all grades through the Grade Centre. Check the course page before each session.
WeBWorK
Carries both practice and assessment. Access is arranged during the first week of classes. Bring a charged laptop to every quiz and examination.
Tutorials
Seven biweekly working sessions run by the teaching assistant. Day, time and room are announced on Blackboard in the first week.
Contact
Individual questions by e-mail to sorujov@ada.edu.az, answered within 48 hours on working days. Office hours Wednesday 16:00-18:00, Building D, Room D325.
Attendance and grading
Attendance follows chapter 6.3 of the University's Student Assessment Regulations; grading follows chapters 6.4 to 6.6. Grading rubrics are provided with each graded assignment.
Academic integrity
Full compliance with the principle of academic integrity is expected. Breaches are handled under the University's Honor Code, and grievances under the Student Academic Grievance Policy.