Course syllabus adopted 2022-02-07 by Head of Programme (or corresponding).
Overview
- Swedish nameSannolikhetsteori och statistisk signalbehandling
- CodeESS012
- Credits7.5 Credits
- OwnerTKELT
- Education cycleFirst-cycle
- Main field of studyMathematics
- DepartmentELECTRICAL ENGINEERING
- GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Course round 1
- Teaching language Swedish
- Application code 50126
- Open for exchange studentsNo
- Only students with the course round in the programme overview.
Credit distribution
Module | Sp1 | Sp2 | Sp3 | Sp4 | Summer | Not Sp | Examination dates |
|---|---|---|---|---|---|---|---|
| 0120 Examination 7.5 c Grading: TH | 7.5 c |
|
In programmes
Examiner
Erik Ström- Full Professor, Communication, Antennas and Optical Networks, Electrical Engineering
Eligibility
General entry requirements for bachelor's level (first cycle)Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Specific entry requirements
The same as for the programme that owns the course.Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Course specific prerequisites
Basic knowledge of elementary functions; linear algebra; calculus; complex numbers; vectors and matrices; linear equation systems; Fourier and Laplace transforms; discrete-time and continuous-time linear systems.Aim
To provide basic knowledge of probability theory and mathematical statistics, foremost from an application perspective, and to provide understanding of the underlying models and approaches. This will give the students insights into how to identify problems that are suitable to be handled with tools from probability and mathematical statistics. The course also aims to give insights into modern statistical signal processing, e.g., digital communication, machine learning, and artificial intelligence.Learning outcomes (after completion of the course the student should be able to)
After completing the course, the student should be able to- explain fundamental probability theory concepts, e.g., probability space, events, probability measures, conditional probability, statistical independence, random variables, cumulative distribution function, probability mass and density functions, and to be able to use these concepts to solve problems
- explain the difference between a frequentist and Bayesian approach
- use Bayes theorem, the law of large numbers, and the central limit theorem in problem solving
- perform point estimation and hypothesis test and assess the performance
- design Matlab-programs to solve statistical signal processing problems
Content
Set theory applied to probability. Probability theory concepts: experiments, outcomes, sample space, events, and probability measure. Probability axioms. Prior, conditional, and posterior probability. Law of total probability. Bayes theorem. Statistical independence. Basic combinatorics: counting methods, binomial and multinomial coefficients. Sampling with and without replacement.Discrete and continuous random variables, cumulative distribution function (CDF), probability mass function (PMF), probability density function (PDF). Expected value, mean, standard deviation, variance, moments. Delta functions and mixed random variables
Families of discrete random variables: Bernoulli, Geometric, Binomial, Pascal, Uniform, Poisson. Families of continuous random variables: uniform, exponential, Erlang, relation between Erlang and Poisson random variables. Gaussian random variables
Multiple random variables. Joint and marginal CDF, PMF, and PDF. Conditional expectation. Bi-variate and multivariate Gaussian random variables. Moment generating functions. Central limit theorem. Markov, Chebyshev and Chernoff inequalities. Law of large numbers.
Point estimation: consistency, bias, mean squared error. Classical and Bayesian estimation. Minimum mean squared error estimation.
Confidence intervals.
Hypothesis testing. Binary hypothesis testing: error types, receiver operating curve. Maximum a posteriori, minimum cost, Neyman-Pearson and maximum likelihood tests. Multiple hypothesis test.
Linear regression.
Organisation
Lectures and problem solving exercise sessions. Project. Written exam.
Literature
Roy D. Yates, and David J. Goodman, Probability and Stochastic Processes, 3rd Edition, International student version, Wiley 2015. ISBN 978-1-118-80871-9.Examination including compulsory elements
Passing the course requires that both the project and written exam are passed. Credit from project and exam is used to assign the final grade.
The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.