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Syllabus:

Computer Engineering MA, Probability and Random Processes, 6 credits


General data

Code: DT049A
Subject/Main field: Datateknik
Cycle: Second cycle
Credits: 6
Progressive specialization: A1N - Second cycle, has only first-cycle course/s as entry requirements
Answerable department: Department of Information Systems and Technology
Answerable faculty: Faculty of Science, Technology and Media
Established: 2/14/2018
Date of change: 2/19/2018
Version valid from: 7/1/2018

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 selectionprocess 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

5.0 credits, T101: Written exam
Grades: A, B, C, D, E, Fx and F. A-E are passed and Fx and F are failed.

1.0 credit, L101: Labs
Grades: Pass or Fail

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

The grades A, B, C, D, E, Fx and F are given on the course. On this scale the grades A through E represent pass levels, whereas 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