FIK3617 Probability and Stochastic Processes for Engineering Applications 9.0 credits

Sannolikhets och stokastiska processer för ingenjörstillämpningar

Offering and execution

Course offering missing for current semester as well as for previous and coming semesters

Course information

Content and learning outcomes

Course contents *

Review of Basic Probability:  Probability spaces, random variables, distribution and density functions, expectation, characteristic functions, conditional probability, conditional expectation.
Sequences of Random Variables:  Convergence concepts, laws of large numbers, central limit theorem.
Basic Concepts of Stochastic Processes:  General concepts, types of stationarity, properties of stochastic processes, systems with stochastic inputs.
Random Processes in Linear Systems:  Spectral analysis of random processes in linear systems, spectral representation and Fourier transforms.
Special Processes:  Markov processes, Wiener Process, Poisson processes, shot noise, thermal noise.
Spectral Representation of Random Processes:  White-noise integrals, expansion of random processes
Applications:  Signal detection and parameter estimation

Intended learning outcomes *

The course is a first graduate (PhD) course in probability and stochastic processes. The course aims at providing the student with a good review of probability theory, and random variables. The course then has its focus on stochastic processes with special attention on applications in wireless communication and signal processing.
After the course the student should be able to:
- model signals and phenomena in a probabilistic manner.
- optimize performance in statistical terms.
- use analytical tools that are useful in the study of stochastic models that appear in wireless communications and other engineering fields.
- predict system performance using statistical reasoning, and verify it using numerical methods.

Course Disposition

The course is a self-study course with weekly meetings where, solutions to homework problems are reviewed by the students.  For each session, a “teacher on duty” is assigned that can help if problems arise. Every student should submit his/her solutions to the “teacher on duty” prior to the meeting. During the meeting the students take turns to present their solution to the problems of the week. If problems occur, e.g. no student is able to come up with a solution or if serious doubts regarding any solution remain, the students should call on the “teacher on duty”.

Literature and preparations

Specific prerequisites *

The course is a first year doctoral course

Basic university level course in probability and statistics.

Recommended prerequisites

Basic university level course in probability and statistics.


No information inserted


Davenport, “Probability and Random Processes”, McGraw-Hill 1970, Classic textbook reissue 1987

Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale *

P, F

Examination *

    Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

    The examiner may apply another examination format when re-examining individual students.


    Other requirements for final grade *

    To pass the course you need to correctly solve 75% or more of the homework problems, or written final exam.

    Opportunity to complete the requirements via supplementary examination

    No information inserted

    Opportunity to raise an approved grade via renewed examination

    No information inserted


    Slimane Ben Slimane

    Ethical approach *

    • All members of a group are responsible for the group's work.
    • In any assessment, every student shall honestly disclose any help received and sources used.
    • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

    Further information

    Course web

    Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

    Course web FIK3617

    Offered by

    EECS/Communication Systems

    Main field of study *

    No information inserted

    Education cycle *

    Third cycle

    Add-on studies

    No information inserted

    Postgraduate course

    Postgraduate courses at EECS/Communication Systems