ACADEMICS
Course Details
ELE320 - Probability and Statistics
2024-2025 Fall term information
The course is not open this term
ELE320 - Probability and Statistics
| Program | Theoretıcal hours | Practical hours | Local credit | ECTS credit |
| Undergraduate | 3 | 0 | 3 | 5 |
| Obligation | : | Must |
| Prerequisite courses | : | MAT123 |
| 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 and to establish thebasis toacquire the skills of statistical inference. |
| Learning outcomes | : | 1. Know the basic concepts of probability theory; 2. Use common probability distributions and analyze their properties; 3. Compute conditional probability distributions and conditional expectations; 4. Compute distributions by use of transformation techniques and solve problems. 5. Use the classical statistical inference techniques for estimation and hypothesis testing |
| 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; Probability and statistics, classification of statistical inference problems; Parameter estimation, properties of estimators, maximum likelihood estimation, confidence interval; Linear regression; Binary hypothesis testing, type-1 and type-2 error probabilities, likelihood ratio test, Neyman-Pearson rule; Significance testing; Generalized likelihood ratio and goodness of fit tests |
| References | : | Bertsekas, Dimitri P., and John N. Tsitsiklis. Introduction to probability. 2nd Ed. Athena Scientific, 2008;Chan, Stanley H. Introduction to Probability for Data Science, Michigan Publishing, 2021; 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 concep |
| 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 | Statistical inference, maximum likelihood parameter estimation, confidence interval |
| 12 | Linear regression |
| 13 | Binary hypothesis testing, type-1 and type-2 error probabilities, maximum likelihood ratio test, Neyman-Pearson rule |
| 14 | Significance testing, Generalized likelihood ratio and goodness of fit tests |
| 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