The goal of this course is to provide an introduction to the basic ideas and concepts from probability theory and mathematical statistics. In addition to a mathematically rigorous treatment, also an intuitive understanding and familiarity with the ideas behind the definitions are emphasized. Measure theory is not used systematically, but it should become clear why and where measure theory is needed.
Probability: Chapters 1-12 from the book Fundamentals of Probability: A First Course by Anirban DasGupta
Statistics: Chapter 8 and 9 from the book "Mathematical Statistics and Data Analysis" by John Rice.
| Lecture time | Room |
|---|---|
| Tuesday 10:15-11:55 | CAB G 61 |
| Thursday 13:15-15:00 | HG E 5 |
Updated 18.03.19 The program will be updated during the semester. Please make sure you have the latest version.
Note 18.03.19 Chapter 5 (generating functions) will not be discussed in lectures, but it will be studied through exercises.
| Lecture | Date | Topics |
|---|---|---|
| 1 | Tue 19.02 | Chapter 1 of AD, Introduction, counting methods |
| 2 | Thu 21.02 | Chapter 1 of AD, Introduction, counting methods |
| 3 | Tue 26.02 |
Chapter 2 of AD, Birthday and matching problem (*) Stirling's approximation |
| 4 | Thu 28.02 | Chapters 2 and 3 of AD, Conditional probability, independence |
| 5 | Tue 05.03 |
Chapters 3 and 4 of AD, discrete random variables (*) Other fundamental moment inequalities |
| 6 | Thu 07.03 |
Chapter 4 of AD, discrete random variables (+) Overview of measurability |
| 7 | Tue 12.03 | Chapter 4 of AD, discrete random variables |
| 8 | Thu 14.03 |
Chapter 4 of AD, discrete random variables (+) Jensen's inequality |
| 9 | Tue 19.03 | Chapters 4 and 6 of AD, standard discrete distributions |
| 10 | Thu 21.03 | Chapter 6 of AD |
| 11 | Tue 26.03 |
Chapter 6 of AD (+) Overview of Kolmogorov's extension theorem |
| 12 | Thu 28.03 |
Chapter 6 of AD (+) Overview of Poisson processes |
| 13 | Tue 02.04 |
Chapter 6 of AD (+) Domination of measures, Radon-Nikodym derivative |
| 14 | Thu 04.04 |
Chapters 7 and 8 of AD (+) Absolute continuity with respect to Lebesgue measure |
| 15 | Tue 09.04 |
Chapters 7 and 8 of AD (+) Review of integrals with respect to a measure |
| 16 | Thu 11.04 | Chapters 7 and 8 of AD |
| 17 | Tue 16.04 | Chapters 7&8, chapters 9&10 of AD |
| 18 | Thu 18.04 |
Chapters 9 and 10 of AD A 15min movie about Carl Friedrich Gauss |
| Tue 23.04 | EASTER BREAK | |
| Thu 25.04 | EASTER BREAK | |
| 19 | Tue 30.04 | Chapters 10 and 11 of AD |
| 20 | Thu 02.05 |
Chapter 11 of AD (x) Continuity correction |
| 21 | Tue 07.05 |
Chapters 11 and 12 of AD (x) 11.5 on the Multivariate case (joint MGF, multinomial distribution, etc.) |
| 22 | Thu 09.05 |
Chapter 12 of AD (x) 12.5 on Bivariate normal conditional distributions (x) 12.6 on Order statistics |
| 23 | Tue 14.05 |
Chapter 12 of AD Chapter 8 of JR: estimators, moment estimators, MLE |
| 24 | Thu 16.05 | Chapter 8 of JR: Large sample theory for the MLE |
| 25 | Tue 21.05 | Chapter 8 of JR: Efficiency, sufficiency |
| 26 | Thu 23.05 |
Chapter 9 of JR (Hypothesis testing): Introduction, Neyman-Pearson Lemma. (x) 8.6 on the Bayesian approach |
| 27 | Tue 28.05 |
Neyman-Pearson Lemma (continued), examples of testing simple hypotheses (x) Sections 9.3 to 9.10 |
UPDATE 01 Mar 2019: Class registrations through the echo system, available on echo.ethz.ch, have now closed. In case of questions, please contact the coordinator.
Solutions should be submitted to your assistant's folder in the box dedicated to this course, next to HG G 53.2. The deadline is 2pm of the Friday before the corresponding class in order to guarantee that they are marked in time. The marked exercise sheets will be returned in the next class or otherwise returned to the box for collection.
The exercises will be uploaded here one week in advance, together with the solutions for the previous sheet. Submitting solutions is not mandatory, but attempting to solve the sheets is very helpful with practicing the contents of the course and preparing for the exam.
| Exercise sheet | Due by | Solution |
|---|---|---|
| Sheet 1 | 01 March 2019 | Solutions 1 |
| Sheet 2 | 08 March 2019 | Solutions 2 |
| Sheet 3 | 15 March 2019 | Solutions 3 |
| Sheet 4 | 22 March 2019 | Solutions 4 |
| Sheet 5 | 29 March 2019 | Solutions 5 |
| Sheet 6 | 4 April 2019 | Solutions 6 |
| Sheet 7 | 11 April 2019 | Solutions 7 |
| Sheet 8 | 29 April 2019 by 12:00 | Solutions 8 |
| Sheet 9 | 3 May 2019 | Solutions 9 |
| Sheet 10 | 10 May 2019 | Solutions 10 |
| Sheet 11 | 17 May 2019 | Solutions 11 |
| Sheet 12 | 24 May 2019 | Solutions 12 |
| Sheet 13 | 31 May 2019 | Solutions 13 |
| Time | Room | Assistant | Contact | Teaching language |
|---|---|---|---|---|
| Tuesday 13-15 | CAB G 56 | Marcello Longo | longom@student.ethz.ch | en |
| Tuesday 13-15 | CHN E 42 | Raphael Oberli | oberlir@ethz.ch | en |
| Tuesday 13-15 | HG E 22 | David Pires Tavares Martins | david.martins@math.ethz.ch | en |
| Tuesday 13-15 | HG E 33.5 | Angelo Abaecherli | angelo.abaecherli@math.ethz.ch | en |
| Tuesday 13-15 | HG G 26.3 | Chong Liu | chong.liu@math.ethz.ch | en |
The first classes will be held on the second week of the semester (26 February 2019).
Grades for this course will be based solely on the written final exam, to be held during the August examination session. The exam will cover all the material taught in the lectures, and will be broadly similar in content to the problems appearing on the exercise sheets.
Students may not bring any paper or calculators to the exam, and should only bring writing materials (pens etc.) along with their student cards (Legi). Paper for drafts and for writing your answers will be provided. You will also be provided with a printed copy of the following formulae sheet:
Some old exams can be found here on the homepage of Group 3. It is not advisable to prepare from old exams only, since the topics covered in previous years may not match exactly the contents from the current course.
For questions before the exam, please attend one of the Präsenz sessions during the semester break. During the second and the third week of the semester after the exam, you have the possibility to look at your exam during the regular Präsenz hours.
Other references include:
