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.
Every session has a problem set of its own on WeBWorK — two a week, one per lecture, twenty problems each. The problems are randomised, so each student receives a different version and gets immediate feedback, and a practice copy of each set is posted beside that session's slides in the course plan below. Alongside the lectures, the teaching assistant runs seven tutorials in alternate weeks, 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% Two each weekQuiz I
10% 17 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% 23 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.
Probability calculator. Students may use the Math Stat I Calculator during Midterm Examination I. It does the long arithmetic of Chapters 1–3: binomial, geometric and negative binomial probabilities, events and Bayes’ rule, and exact counting, with the matching R command beside each answer. A six-minute video guide shows how to use it, followed by a worked example on the negative binomial.
Problem sets
Each lecture has its own set on WeBWorK. The set for a Wednesday lecture is ps1 for that week and the set for the Saturday lecture is ps2; both open when they are published, before their lecture, and close at 23:59 on the Sunday of the week after their lectures, so there is always more than a full week to work on each. Attempts before the deadline are unlimited. Two copies of every set are linked beside the slides in the course plan below: a practice copy of the problems, and a solutions copy of the same problems worked through in full with an answer key at the end. Both carry their own randomly generated numbers, so the figures in them will not match your own copy on WeBWorK — which is the point. Follow the method, not the arithmetic.
| Week | Sessions | ps1 covers | ps2 covers | Both close |
|---|---|---|---|---|
| 1 | 9 and 12 September | §§1.1–1.2 | §§1.3–1.6 | 27 September |
| 2 | 16 and 19 September | §§2.1–2.5 | §2.6 | 4 October |
| 3 | 23 and 26 September | §2.7 | §2.8 | 4 October |
| 4 | 30 September and 3 October | §2.9 | §2.10 | 11 October |
| 5 | 7 and 10 October | §§2.11–2.13 | §§3.1–3.3 | 18 October |
| 6 | 14 and 17 October | §3.4 | §§3.5–3.6 | 25 October |
| 7 | 21 October | §§3.7–3.8 | — | 1 November |
| 8 | 28 and 31 October | §3.9 | §§3.10–3.11 | 8 November |
| 9 | 4 and 7 November | §§4.1–4.2 | §§4.3–4.4 | 15 November |
| 10 | 11 and 14 November | §4.5 | §4.6 | 22 November |
| 11 | 18 and 21 November | §§4.7–4.8 | §§4.9–4.11 | 29 November |
| 12 | 25 and 28 November | §§5.1–5.2 | §5.3 | 6 December |
| 13 | 2 and 5 December | §5.4 | §§5.5–5.7 | 13 December |
| 14 | 9 and 12 December | §5.8 | §5.9 | 20 December |
| 15 | 16 and 19 December | §§5.10–5.11 | §5.12 and Chapters 1–5 review | 27 December |
Week 7 carries a single set, because its second session is Midterm Examination I rather than a lecture.
Course plan
| Date | Topic | Reading and preparation | Materials |
|---|---|---|---|
| 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., §§1.1–1.2. 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 §§1.3–1.6. Exercises at the end of §1.3, and the Chapter 1 supplementary exercises. | |
| 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. Tutorial week: TA-led tutorial this week. | |
| 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 §§2.11–2.13. 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. Tutorial week: TA-led tutorial this week. | |
| 14 October | The binomial distribution: derivation from Bernoulli trials, mean, variance, and use in counting defaults and defects. | Wackerly §3.4. Exercises at the end of §3.4. | |
| 17 October | Quiz I on WeBWorK, first 30 minutes of class (Chapters 1–2). The geometric and negative binomial distributions: waiting for the first success and for the rth success; memorylessness in discrete time. | Prepare Wackerly Chapters 1–2 for the quiz. Reading for the lecture: §§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). Tutorial week: TA-led tutorial this week. | |
| 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. Tutorial week: TA-led tutorial this week. | |
| 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. Tutorial week: TA-led tutorial this week. | |
| 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 §§5.5–5.7. Exercises at the end of §§5.5–5.7. Tutorial week: TA-led tutorial this week. | |
| 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. | Wackerly §5.8. Exercises at the end of §5.8. | |
| 12 December | Quiz II on WeBWorK, first 30 minutes of class (Chapter 4 and §§5.1–5.8). The multinomial distribution. | Prepare Wackerly Chapter 4 and §§5.1–5.8 for the quiz. Reading for the lecture: §5.9. | |
| 16 December | The bivariate normal distribution. Conditional expectations and the regression function; the law of iterated expectations and the conditional-variance decomposition. | Wackerly §§5.10–5.11. Exercises at the end of §5.11. Tutorial week: TA-led tutorial this week. | |
| 19 December | Chapter 5 synthesis and comprehensive review of Chapters 1–5 in preparation for Midterm Examination II. | Wackerly §5.12. Supplementary exercises, Chapter 5. | |
| 23 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 working sessions in alternate weeks, 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.