Course syllabus

Course PM

ESS013 Sannolikhetsteori och statistisk signalbehandling LP4 VT24 (7,5 hp)

The course is offered by the Dept. of Electrical Engineering. The formal course plan is found at the Student Portal


The official language of the course is Swedish. Nevertheless, written course material (text book, slides, assignments, etc.) will be in English for several reasons, including preparing students for an engineering career, which today requires a good command of English and knowledge of English terminology. Spoken language at lectures, exercises, etc. will be Swedish, except when the teacher is not fluent in Swedish.


Student course representatives are

Communication with teachers can be via email (preferred) or via Canvas. Please mark emails with [ESS013] in the subject heading.

Questions about quizzes, programming assignments, project and exercises are directed to Björn or Kaan. Questions about lectures or course organization, grades, or other general matters are directed to Erik. 

Examiner and lecturer:

Teaching assistants:

Aims and objectives

The course aims to provide basic knowledge of probability and mathematical statistics, primarily from an application point of view, and to give understanding of the underlying models and approaches. Special emphasis is put on interpretation and modeling such that the course theory will be useful for future courses and to solve engineering problems in practice. Connections to problems in modern statistical signal processing, e.g., digital communication, machine learning and artificial intelligence will be provided.


The schedule is, of course, available in TimeEdit. Lectures and exercises content and deadlines for quizzes, programming assignments, and project are found in the Week Plan.

Text books

  • Roy D. Yates, and David J. Goodman, Probability and Stochastic Processes, 3rd Edition, International student version, Wiley 2015. ISBN 978-1-118-80871-9. Available at Cremona.
  • Gareth James, Daniela Witten, Trevor Hastie, and Robert Tibshirani, An Introduction to Statistical Learning, Springer 2013. The E-book version (downloadable pdf) is available through the library Printed books can be bought at your favorite on-line book store.
  • Jonathan Gillard, A First Course in Statistical Inference, Springer 2020. The E-book version (downloadable pdf) is available through the library Printed books can be bought at your favorite on-line book store. 

Yates and Goodman is the main text, and students are strongly recommended to acquire it. It is an excellent book that will also be useful as a reference in future courses. In addition, students are allowed to bring the book to the exam.

The James, Witten, Hastie, and Tibshirani book will be used to complement Yates and Goodman on material regarding linear regression. It is also an excellent book, but perhaps buying it would not be recommended as a new edition is coming. Finally, the book by Gillard is used to complement Yates and Goodman on material regarding confidence intervals. It is an easy-to-read book that can also be used to give a second presentation on the material in the other books.

Solution manual to Yates and Goodman is available for download in the Files section.

Course organization

The course consists of scheduled lectures and exercises during which the theory is discussed and problems are solved. Reading instructions for lectures and references to problems for exercises are found in the Week Plan.

Students are expected to complete six quizzes, six programming assignments (in MATLAB), and one project. Deadlines for these are found in the Week Plan. The quizzes, programming assignments, and projects are found in the Assignments section. Hand-ins are graded, and scores are counted towards the final grade according to the rules below.

Deadlines are strict. No late hand-ins will be graded, and no extensions will be granted. There will be no possibility of complementing a hand-in after the submission deadline.

Changes since last year

  • The course now consists of two modules
    • Project, 2 hp, grading scheme: pass/fail
    • Written exam, 5.5 hp, grading scheme: fail, 3, 4, 5
  • The course has a new course code (last year, it was ESS012) due to the change in module structure
  • The number of lectures and the content have been modified (material has been removed, added, and redistributed over the lectures)
  • Time synchronization between lectures and exercises has been improved
  • Information about the examination rules has been updated
  • The project grading rules have been updated 

Learning outcomes

After completing the course, the student should be able to (in Swedish, which is the official text)
  • förklara fundamentala begrepp inom sannolikhetsläran, tex. utfallsrum, händelser, sannolikhetsmått, betingad sannolikhet, oberoende, stokastiska variabler, fördelnings- och täthetsfunktion, samt använda dessa begrepp för att lösa problem
  • redogöra för skillnaden mellan en frekventistisk och en Bayesiansk ansats
  • använda Bayes formel, stora talens lag, samt centrala gränsvärdessatsen i problemlösning
  • utföra punktskattning och hypotestest samt uppskatta kvalitén i dessa
  • konstruera Matlab-program för att lösa problem inom statistisk signalbehandling

Learning outcomes in English translation: the student should be able to

  • explain fundamental concepts in probability theory, e.g., sample space, events, probability measure, conditional probability, independence, random variables, probability density function, cumulative density function, and be able to use these concepts to solve problems
  • explain the difference between the frequentist and Bayesian approaches
  • use Bayes theorem, the law of large numbers, and the central limit theorem to solve problems
  • perform point estimation and hypothesis testing, and to estimate the quality in these 
  • design MATLAB-programs to solve statistical signal processing problems 


There are two examination modules: project (2 hp, pass/fail) and exam (5.5 hp, U, 3, 4, 5). To pass the course, students need to pass both modules.

To pass the project module, students need to receive at least 4 points (of 8) on the project. See below for details on the project grading rules.

To pass the exam module, students need to (a) receive at least 20 points on the written exam and (b) receive at least 45 points from the quizzes, programming assignments, project, and written exam. See below for details on points from the quizzes and programming assignments.

Point distribution and rules

Quizzes, programming assignments, and the project are graded and counted toward the final grade. Quizzes and programming assignments are not mandatory but highly recommended.

The maximum scores per quiz, programming assignment, project, and written exam are defined in the table below.

What Instances Max points per instance Max points Min points for passing grade
Quiz  6 3 18 0
Programming assignment 6 3 18 0
Project 1 8 8 4
Written exam* 1 56 56 20
Total 100  (see below for grades)

*) note that to pass the module "exam" and receive 5.5 hp, the total course score must be at least 45 points, of which the written exam score is at least 20 points. 

Points for quizzes, programming assignments, and the project do not expire. That is, they are kept indefinitely until the student passes the course.


The purpose of the project is to facilitate learning of the course material. All team members should contribute equally towards accomplishing the project tasks. Even if the work is split up between group members, the group members are collectively responsible for the results and should be able to answer detailed questions about any part of the project at the project oral exam. 

The project outcome should be documented in a short report, which is due a few days before the oral exam (see Week Plan). The report should be written in English and comply with standard practices for technical reports, see Chalmers Writing Guide for advice. The report should fully document the project, i.e., explain what was done, why it was done, and what the results were. A section in the report should clearly state the contribution of each group member, including report writing and programming. The report should be concise: a report that is too long or verbose will not give full points. Background material should be limited to a minimum. The purpose of the report is to document the project group work, not someone else’s work. Chatbots like ChatGPT can be used to assist in writing the report, but not for programming. The group members are fully responsible for the correctness of the text, regardless of if chatbots are used or not. 

The program code needed to solve the project should be carefully commented on and should be attached to the report. Writing program code is an efficient way to learn. Hence, all programs should be written from scratch. It is prohibited to copy code from the Internet or other sources or use chatbots like ChatGPT. Such practice will be considered cheating and is subject to disciplinary action. 

Cooperation between groups is considered cheating and is subject to disciplinary action.

The project is graded according to the following guidelines. 

  • Report: The report should document the project, be concise, easy to follow, written in good English, and comply with the Chalmers Writing Guide. Results should be commented on and checked to be reasonable and consistent with theory. Plots must be clearly labeled with units. Late reports will not be graded (see Week Plan for submission deadline). It is not allowed to complement a report after the submission deadline. The maximum report score is 6 points.  
  • Oral exam: All members of the group should be able to explain and defend all details about the project report at the oral exam. For example, suppose Student A has programmed a MATLAB function; then Student B and C should be able to explain the code in the oral exam. Only groups that have submitted the report before the deadline can take the oral exam.  The maximum oral exam score is 2 points. The oral exam is mandatory.

The report score is common to all group members, while the oral exam score is assigned individually. The total project score can therefore be different for the different group members.

A project score of less than 4 points will cause the project to be graded as failed.

Students who fail the project can hand in an improved report to possibly achieve a passing grade (4 points). Note that a student can get at most 4 points in total for the report after improving it.

Students with failing project grades must pass the project the next academic year.

Written exam

Exam grading policy: An erroneous answer or incomplete or poorly motivated solutions give point reductions down to a minimum of 0 points.  As a general rule, bad motivation or errors related to the course's fundamental principles will lead to larger point reductions. Computational errors that do not lead to unreasonable answers generally give smaller reductions.

Assuming that the exam will take place on campus, the allowed material

  • Chalmers-approved calculator
  • L. Råde, B. Westergren. Beta, Mathematics Handbook, any edition. Notes are not allowed in the book. 
  • Roy D. Yates, and David J. Goodman, Probability and Stochastic Processes, 3rd Edition, International student version, Wiley 2015. Notes are not allowed in the book, except for
    • Correction of errors in the books
    • Highlights or underlining
    • Stickers for quick indexing and finding of material in the books (including labeling of the stickers)
  • One A4 page with your own handwritten notes. Both sides of the page can be used. Photocopies, printouts, other students' notes, or any other material are not allowed.
  • A paper-based dictionary without added notes (electronic dictionaries are not allowed).

See Week Plan for the likely date for the exam. Please check LADOK for definitive information about date and time. 

Final grades

To pass the written exam module, a student must have acquired at least 20 points on the written exam. If this is the case, then the final grade is set according to the following table.

Stot = Total score (quizzes, programming assignments, project, exam) Grade
Stot < 45 U
Stot LaTeX: \in [45, 65)  3
Stot LaTeX: \in [65, 80) 4
Stot LaTeX: \in [80, 100] 5

Note that quizzes and programming scores are counted towards the final grade. It is highly recommended to complete these. A relatively high exam score is otherwise needed to reach a passing grade.


Course summary:

Date Details Due