ACADEMICS
Course Details
ELE609 - Probability Theory and Stochastic Processes
2024-2025 Fall term information
The course is not open this term
ELE609 - Probability Theory and Stochastic Processes
| Program | Theoretýcal hours | Practical hours | Local credit | ECTS credit |
| MS | 3 | 0 | 3 | 8 |
| Obligation | : | Elective |
| Prerequisite courses | : | - |
| Concurrent courses | : | - |
| Delivery modes | : | Face-to-Face |
| Learning and teaching strategies | : | Lecture, Question and Answer, Problem Solving |
| Course objective | : | After introducing the basic concepts of the probability theory in the undergraduate study, in this course the theory is presented with sufficient elaboration supported with many engineering oriented examples. With this it is aimed to have the students build a solid understanding of the concepts and establish an ability to solve the problems by using these concepts as a tool. |
| Learning outcomes | : | Knows the basic components of probability model. Knows how to model the sample space in an experiment Computes the statistical properties (mean, variance, covariance, correlation) of a given one/multi variable random variable(s). Have the knowledge to follow and understand the advanced and complex probability theory related concepts. In engineering problems recognizes the random phenomena and applies the correct statistical models. |
| Course content | : | The Axioms of Probability, Probability Space Conditional probability, Bernoulli trials The Concept of a Random Variable Distribution and density functions, Conditional distributions Asymptotic approximations for binomial random variables Functions of one random variable, Transformation of a random variable Mean and Variance Concepts, Moments, Characteristic Functions Two random variables, Bivariate distributions One function of two random variables Two functions of two random variables (Jacobian matrix) Joint Moments, Joint Characteristic Functions, Conditional Bivariate Distributions Random Processes, Wide Sense and Complete Stationarity, Statistical averages and ergodicity Autocorrelation and cross-correlation functions, Gauss processes |
| References | : | Papoulis and Pillai, Probability, Random Variables, and Stochastic Processes, ; 4th Ed., Mc-Graw Hill, 2002.; Milton and Arnold, Introduction To Probability and Statistics, 4th Ed., ; Mc-Graw Hill, 2003. |
| Weeks | Topics |
|---|---|
| 1 | The Axioms of Probability, Sample Space, Conditional Probability |
| 2 | Independence, Bernoulli Trials |
| 3 | Random Variable Concept |
| 4 | Distribution and Density Functions, Conditional Distributions |
| 5 | Asymptotic Approximations for Binomial Random Variables |
| 6 | Functions of One Random Variable, Transformation of a Random Variable |
| 7 | Mean and Variance Concepts, Moments, Characteristic Functions |
| 8 | Midterm Exam |
| 9 | Two Random Variables, Bivariate Distributions |
| 10 | One Function of Two Random Variables |
| 11 | Two Functions of Two Random Variables (Jacobian Matrix) |
| 12 | Joint Moments, Joint Characteristic Functions, Conditional Bivariate Distributions |
| 13 | Random Processes and their properties, Stationarity, Statistical averages and ergodicity |
| 14 | Autocorrelation and cross-correlation functions, Gauss processes |
| 15 | Preparation Week for Final Exams |
| 16 | Final exam |
| Course activities | Number | Percentage |
|---|---|---|
| Attendance | 0 | 0 |
| Laboratory | 0 | 0 |
| Application | 0 | 0 |
| Field activities | 0 | 0 |
| Specific practical training | 0 | 0 |
| Assignments | 0 | 0 |
| Presentation | 0 | 0 |
| Project | 0 | 0 |
| Seminar | 0 | 0 |
| Quiz | 0 | 0 |
| Midterms | 1 | 50 |
| Final exam | 1 | 50 |
| Total | 100 | |
| Percentage of semester activities contributing grade success | 50 | |
| Percentage of final exam contributing grade success | 50 | |
| Total | 100 | |
| Course activities | Number | Duration (hours) | Total workload |
|---|---|---|---|
| Course Duration | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Specific practical training | 0 | 0 | 0 |
| Field activities | 0 | 0 | 0 |
| Study Hours Out of Class (Preliminary work, reinforcement, etc.) | 14 | 8 | 112 |
| Presentation / Seminar Preparation | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework assignment | 0 | 0 | 0 |
| Quiz | 0 | 0 | 0 |
| Midterms (Study duration) | 1 | 42 | 42 |
| Final Exam (Study duration) | 1 | 44 | 44 |
| Total workload | 30 | 97 | 240 |
| Key learning outcomes | Contribution level | |||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1. | Has general and detailed knowledge in certain areas of Electrical and Electronics Engineering in addition to the required fundamental knowledge. | |||||
| 2. | Solves complex engineering problems which require high level of analysis and synthesis skills using theoretical and experimental knowledge in mathematics, sciences and Electrical and Electronics Engineering. | |||||
| 3. | Follows and interprets scientific literature and uses them efficiently for the solution of engineering problems. | |||||
| 4. | Designs and runs research projects, analyzes and interprets the results. | |||||
| 5. | Designs, plans, and manages high level research projects; leads multidiciplinary projects. | |||||
| 6. | Produces novel solutions for problems. | |||||
| 7. | Can analyze and interpret complex or missing data and use this skill in multidiciplinary projects. | |||||
| 8. | Follows technological developments, improves him/herself , easily adapts to new conditions. | |||||
| 9. | Is aware of ethical, social and environmental impacts of his/her work. | |||||
| 10. | Can present his/her ideas and works in written and oral form effectively; uses English effectively. | |||||
1: Lowest, 2: Low, 3: Average, 4: High, 5: Highest