Computer Engineering MA, Probability and Random Processes, 6 credits
Please note that the literature can be changed/revised until:
• June 1 for a course that starts in the autumn semester
• November 15 for a course that starts in the spring semester
• April 1 for a course that starts in the summer
Print or save the syllabus as a PDF
You can easily print a syllabus from the website. Use the keyboard shortcut ctrl+p (Windows) or command+p (Mac). In the next step, you choose whether you want to print or save the course plan as a PDF.
Syllabus:
Datateknik AV, Sannolikhetslära och stokastiska processer, 6 hp
Computer Engineering MA, Probability and Random Processes, 6 credits
General data
- Code: DT049A
- Subject/Main field: Computer Engineering
- Cycle: Second cycle
- Credits: 6
- Progressive specialization: A1N - Second cycle, has only first-cycle course/s as entry requirements
- Education area: Teknik 100%
- Answerable faculty: Faculty of Science, Technology and Media
- Answerable department: Information Systems and Technology
- Approved: 2018-02-19
- Date of change: 2021-08-05
- Version valid from: 2021-07-01
Aim
The course presents the fundamental of probability theory and random processes needed by students in computer science, communications, signal processing and other disciplines.
Course objectives
The student should after completed course be able to:
- define and use the concepts of probability space, random variable, and random process, and know a number of concrete examples of the concepts,
- define and use Markov chains in discrete and continuous time,
- describe the various modes of convergence of random variables and their implications,
- use the law of large numbers and the martingale convergence theorem to assess asymptotic convergence properties of random variables,
- explain and apply the concepts of stationary stochastic processes, spectral methods for stationary processes,
- understand and apply the concepts of filtering and prediction of a random process,
- relate probability theory to real statistical analysis.
Content
- Probability review: probability spaces, axioms of probability, conditional probabilities, independence, random variables, expectation, conditional expectation, inequalities.
- Limit theorems – laws of large numbers, central limit theorems.
- Poisson Process – memoryless properties, alternative definitions, combining and splitting.
- Finite State Markov chains – first passage time analysis, steady-state analysis
- Gaussian Processes – jointly Gaussian random variables, covariance matrices, filtered processes, power spectral density.
- Bayesian Estimation – MMSE criteria, estimation and Gaussian random vectors, linear least squares estimation.
Entry requirements
Computer Engineering BA (AB), 45 credits including programming. Mathematics BA (A), 22.5 credits, including a course in statistics and linear algebra.
Selection rules and procedures
The selection process is in accordance with the Higher Education Ordinance and the local order of admission.
Teaching form
Teaching is performed through lectures, exercises and laboratory work
Examination form
L101: Labs, 1 Credits
Grade scale: Fail (U) or Pass (G)
T101: Written exam, 5 Credits
Grade scale: Seven-grade scale, A, B, C, D, E, Fx and F. Fx and F represent fail levels.
Grading criteria for the subject can be found at www.miun.se/gradingcriteria.
The examiner has the right to offer alternative examination arrangements to students who have been granted the right to special support by Mid Sweden University’s disabilities adviser.
Grading system
Seven-grade scale, A, B, C, D, E, Fx and F. Fx and F represent fail levels.
Course reading
Required literature
- Author: Robert G. Gallager
- Title: Stochastic Processes: Theory for Applications
- Publisher: Cambridge University Press, 2014.
- Comment: ISBN 9781107039759
Reference literature
- Author: Hisashi Kobayaski, Brian L Mark, and William Turin
- Title: Probability, Random Processes, and Statistical Analysis
- Publisher: Cambridge University Press
- Comment: ISBN 9780521895446