Computer Engineering Ma, Probability and Random Processes, 6 credits

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 and Markov fields,
• 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
• Markov fields.
• 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: Two-grade scale

T101: Written exam, 5 Credits
Grade scale: Seven-grade scale, A-F o Fx

Link to subject-specific grading criteria: 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.

Examination restrictions

Students are entitled to three examination opportunities within one year according to the examination format given in this version of the course syllabus. After the one-year period, the examination format given in the most recent version of the course syllabus applies.

Grading system

Seven-grade scale, A-F o Fx