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406-2604-AAL 8 Credits MSC D-MATH
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Probability and Statistics

Lecturers & Examiners: Prof. Dr. Vincent Tassion
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
VVZ CR n/a

Last Updated: 2026-02-05 16:29:35

Abstract

- Probability spaces- Discrete models, Randiom walk- Conditional probabilities, independence- Continuous models- Limit theorems- Methods of moments- Maximum likelihood estimation- Hypothesis testing- Confidence intervals- Introductory Bayesian statistics- Linear regression model

Objective

The first part of the course gives an overview of the main concepts needed to understand probability theory (sample spaces, discrete models, random walk, contiuous models and limit theorems such as the Laws of Large Numbers and the Central limit theorem). It will be based on the German script "Wahrscheinlichkeitsrechnung und Statistik". The second part covers some fundamental results of mathematical statistics including estimation methods, hypothesis testing as well as the linear regression model. For this part, we will use the script "Statistics for Mathematics". Both scripts are available at https://www.stat.math.ethz.ch/~fadouab/

Content

Probability: Chapters 1-5 (Probabilities and events, Discrete and continuous random variables, Generating functions) and Sections 7.1-7.5 (Convergence of random variables) from the book "Probability and Random Processes". Most of this material is also covered in Chap. 1-5 of "Mathematical Statistics and Data Analysis", on a slightly easier level. Statistics: Sections 8.1 - 8.5 (Estimation of parameters), 9.1 - 9.4 (Testing Hypotheses), 11.1 - 11.3 (Comparing two samples) from "Mathematical Statistics and Data Analysis".

Resources

Lecture Notes

(*) Wahrscheinlichkeitsrechnung und Statistik(*) Statistics for MathematicsBoth scripts can be found athttps://www.stat.math.ethz.ch/~fadouab/

Literature

A. DasGupta, Fundamentals of Probability: A First Course, Springer (2010) R. Berger and G. Casella, Statistical Inference, Duxbury Press (1990) J. A. Rice, Mathematical Statistics and Data Analysis, Wadsworth, second edition (1995) H.-O. Georgii, Stochastik, de Gruyter, 5. Auflage (2015) A. Irle, Wahrscheinlichkeitstheorie und Statistik, Teubner (2001)

General Information

Language
English
Levels
MSC
Frequency
Semesterly recurring

Examination

Type
session examination
Mode
written 180 minutes
Aids
None

Course Components

Type Title Time & Place Hours
revision course / private study Probability and Statistics
Self-study course. No presence required.
No time listed 240 h semesterly

Offered In