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
FIK3617 Probability and Stochastic Processes for Engineering Applications 9.0 credits
Information per course offering
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Course syllabus as PDF
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Course syllabus FIK3617 (Spring 2016–)Content and learning outcomes
Course contents
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.
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.
Literature
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
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.
Pass/Fail
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.
Examiner
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.