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ESS012 Sannolikhetsteori och statistisk signalbehandling LP4 VT23 (7,5 hp)

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

Language

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.

Contact

Student course representatives are

Communication with teachers can be via email (preferred) or via Canvas. Please mark emails with [ESS012] in the subject heading.

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

Examiner and lecturer:

Teaching assistant:

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.

Schedule

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

Yates and Goodman is the main text and students are strongly recommended to acquire it. It is an excellent book that will be useful also in future courses as a reference. In addition, it it 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 on its way. 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 to complement a hand-in after the submission deadline.

Changes since last year

  • The number of lectures and the content has been modified (material has been removed, added, and redistributed over the lectures)
  • Time synchronization between lectures and exercises has been improved
  • Timing of deadlines have been changed to be coordinated with other courses in the study period
  • Information about the examination rules have 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 

Examination

Point distribution and rules

Quizzes, programming assignments, and project are graded and counted towards the final grade. Quizzes and programming assignments are not mandatory, but highly recommended. The project is mandatory, as it will be used to examine the learning outcome related to MATLAB-programming. 

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)

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

Project

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 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. It 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 too long or verbose report 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.

Program code needed to solve the project should be carefully commented and be attached to the report. Writing program code is an efficient way to learn. Hence, all programs should be written from scratch. That is, it is not allowed to copy code from the Internet or other sources. Such practice will be caught by Urkund and will be 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 and checked that they are 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 at 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. That is, the total project score can be different for the different group members.

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

Students that 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 the report.

Students with failing project grade will have to pass the project the next academic year.

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

Written exam

Exam grading policy: An erroneous answer, incomplete or badly motivated solutions give point reductions down to a minimum of 0 points.  As a general rule, bad motivation or errors that relate to fundamental principles of the course will lead to large 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, with the exception of correction of errors in the book.
  • One A4 page with your own handwritten notes. Both sides of the page can be used. Photo copies, printouts, other students' notes, or any other material is 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 course, a student must

  • Acquired at least 20 points on the written exam
  • Acquired at least 4 points for the project

If the above requirements are fulfilled, 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 that quizzes and programming scores are counted towards the final grade. It is highly recommended to complete these. A relative high exam score is otherwise needed to reach a passing grade.

 

Course summary:

Date Details Due