ACADEMICS
Course Details
ELE302 - Probability Theory
2024-2025 Spring term information
The course is not open this term
ELE302 - Probability Theory
| Program | Theoretıcal hours | Practical hours | Local credit | ECTS credit |
| Undergraduate | 3 | 0 | 3 | 5 |
| Obligation | : | Must |
| Prerequisite courses | : | - |
| Concurrent courses | : | - |
| Delivery modes | : | Face-to-Face |
| Learning and teaching strategies | : | Lecture, Question and Answer, Problem Solving |
| Course objective | : | To introduce the basic concepts of probability theory To have the students acquire the skills to analyze nondeterministic signals by modelling them as random processes. |
| Learning outcomes | : | Know the basic concepts of probability theory. Use common probability distributions and analyse their properties. Compute conditional probability distributions and conditional expectations. Compute distributions by use of transformation techniques and solve problems. Define and use the properties of Stochastic processes, especially Gaussian and Poisson Processes. |
| Course content | : | Introduction and definitions (Set Theory, Experiment, Sample Space, Events) Mathematical model of probability, Joint and conditional probability, Bayes theorem Independent events and Bernoulli trials The random variable concept Probability distribution and density functions Conditional distributions and densities Expected values, moments and characteristic functions Transformations of a single random variable. Multiple random variables, joint distribution and density functions Limit theorems Operations on multiple random variables Definition of a random process Independence and stationarity Time averages, statistical averages and ergodicity Autocorrelation and cross-correlation functions Gauss and Poisson processes |
| References | : | Peebles, Jr., Probability, Random Variables, and Random Signal Principles, 4th Ed.,; McGraw-Hill, 2001. |
| Weeks | Topics |
|---|---|
| 1 | Introduction and definitions (Set Theory, Experiment, Sample Space, Events) |
| 2 | Mathematical model of probability, Joint and conditional probability, Bayes theorem |
| 3 | Independent events and Bernoulli trials |
| 4 | The random variable concept |
| 5 | Probability distribution and density functions, Conditional distributions and densities |
| 6 | Expected values, moments and characteristic functions |
| 7 | Transformations of a single random variable |
| 8 | Midterm |
| 9 | Multiple random variables, joint distribution and density functions |
| 10 | Limit theorems, Operations on multiple random variables |
| 11 | Random processes and their properties |
| 12 | Independence and stationarity of random processes |
| 13 | Time averages, statistical averages and ergodicity, Autocorrelation and cross-correlation functions |
| 14 | Gauss and Poisson processes |
| 15 | Final exam preparation |
| 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 | 40 |
| Final exam | 1 | 60 |
| Total | 100 | |
| Percentage of semester activities contributing grade success | 40 | |
| Percentage of final exam contributing grade success | 60 | |
| 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 | 5 | 70 |
| Presentation / Seminar Preparation | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework assignment | 0 | 0 | 0 |
| Quiz | 0 | 0 | 0 |
| Midterms (Study Duration) | 1 | 18 | 18 |
| Final Exam (Study duration) | 1 | 20 | 20 |
| Total workload | 30 | 46 | 150 |
| Key learning outcomes | Contribution level | |||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1. | Possesses the theoretical and practical knowledge required in Electrical and Electronics Engineering discipline. | |||||
| 2. | Utilizes his/her theoretical and practical knowledge in the fields of mathematics, science and electrical and electronics engineering towards finding engineering solutions. | |||||
| 3. | Determines and defines a problem in electrical and electronics engineering, then models and solves it by applying the appropriate analytical or numerical methods. | |||||
| 4. | Designs a system under realistic constraints using modern methods and tools. | |||||
| 5. | Designs and performs an experiment, analyzes and interprets the results. | |||||
| 6. | Possesses the necessary qualifications to carry out interdisciplinary work either individually or as a team member. | |||||
| 7. | Accesses information, performs literature search, uses databases and other knowledge sources, follows developments in science and technology. | |||||
| 8. | Performs project planning and time management, plans his/her career development. | |||||
| 9. | Possesses an advanced level of expertise in computer hardware and software, is proficient in using information and communication technologies. | |||||
| 10. | Is competent in oral or written communication; has advanced command of English. | |||||
| 11. | Has an awareness of his/her professional, ethical and social responsibilities. | |||||
| 12. | Has an awareness of the universal impacts and social consequences of engineering solutions and applications; is well-informed about modern-day problems. | |||||
| 13. | Is innovative and inquisitive; has a high level of professional self-esteem. | |||||
1: Lowest, 2: Low, 3: Average, 4: High, 5: Highest