| 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 |
Course Outline Weekly
| 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 |
Matrix Of The Course Learning Outcomes Versus Program Outcomes
| 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. | | | | | |
