EE531 PROBABILITY AND STOCHASTIC PROCESSES
| Course Code: | 5670531 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Electrical and Electronics Engineering |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Assoc.Prof.Dr. BARIŞ NAKİBOĞLU |
| Offered Semester: | Fall Semesters. |
Course Objectives
By the end of this course, students will:
- Gain a solid foundation in probability theory and random variables, as a basis for advanced study in stochastic processes.
- Develop an understanding of key classes of stochastic processes, including Poisson, Gaussian, and Markov processes, and their properties.
- Learn techniques for analyzing random signals and systems, including correlation, power spectra, and responses of linear systems to stochastic inputs.
- Build the ability to apply stochastic modeling methods to engineering problems in communications, signal processing, and related fields.
Course Content
Review of probability theory and random variables. Sequence of random variables, convergence concepts. Stochastic processes: correlation and power spectra, stationarity, linear systems with random inputs, second order processes; stochastic continuity, differentiation and integration in quadratic mean; Gaussian processes; Poisson processes, shot noise; Markow processes; orthogonal expansions, least mean square error estimation.
Course Learning Outcomes
Upon successful completion of the course, students will be able to:
-
Recall and apply probability concepts, random variables, and convergence of sequences of random variables.
-
Model and analyze real-world systems using Poisson processes.
-
Characterize Gaussian random vectors and processes; compute correlations, covariances, and power spectra.
-
Formulate problems as finite- and countable-state Markov chains, determine stationary distributions, and analyze long-term behavior.
-
Understand renewal theory and apply it to stochastic models with repeated random events.
-
Apply martingale properties and random walk models to analyze stochastic behavior in time-evolving systems.
-
Employ least mean square error (LMSE) estimation and orthogonal expansions for prediction and filtering in stochastic systems.
-
Develop mathematical maturity and analytical skills in applying theory to novel problems.
Program Outcomes Matrix
| Contribution | |||||
| # | Program Outcomes | No | Yes | ||
| 1 | Depth: Our graduates acquire in depth knowledge in one of the various specialization areas of Electrical and Electronics Engineering, they are informed about current scientific research topics and they implement innovative methods. | ✔ | |||
| 2 | Breadth: Our graduates get familiarized in other subspecialty areas related to their specialization in Electrical and Electronics engineering and/or relevant areas in other disciplines. | ✔ | |||
| 3 | Research: Our graduates acquire the skills to conduct and to complete scientific research by accessing contemporary knowledge in their specialty areas. | ✔ | |||
| 4 | Life-long learning: Our graduates develop their life-long learning habits. | ✔ | |||
| 5 | Communication skills: Our graduates concisely communicate their ideas and work related results in written and oral form. | ✔ | |||
| 6 | Ethics: Our graduates internalize rules of research and publication ethics as well as professional ethics. | ✔ | |||