ACADEMICS
Course Details
ELE 609 Probability Theory and Stochastic Processes
2020-2021 Spring term information
The course is not open this term
Timing data are obtained using weekly schedule program tables. To make sure whether the course is cancelled or time-shifted for a specific week one should consult the supervisor and/or follow the announcements.
Course definition tables are extracted from the ECTS Course Catalog web site of Hacettepe University (http://akts.hacettepe.edu.tr) in real-time and displayed here. Please check the appropriate page on the original site against any technical problems. Course data last updated on 01/03/2021.
ELE609 - PROBABILITY THEORY and RANDOM PROCESSES
| Course Name | Code | Semester | Theory (hours/week) |
Application (hours/week) |
Credit | ECTS |
|---|---|---|---|---|---|---|
| PROBABILITY THEORY and RANDOM PROCESSES | ELE609 | Any Semester/Year | 3 | 0 | 3 | 8 |
| Prerequisite(s) | None | |||||
| Course language | Turkish | |||||
| Course type | Elective | |||||
| Mode of Delivery | Face-to-Face | |||||
| Learning and teaching strategies | Lecture Question and Answer Problem Solving | |||||
| Instructor (s) | Department Faculty | |||||
| 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 |
| |||||
| 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. | |||||
Course outline weekly
| Weeks | Topics |
|---|---|
| Week 1 | The Axioms of Probability, Sample Space, Conditional Probability |
| Week 2 | Independence, Bernoulli Trials |
| Week 3 | Random Variable Concept |
| Week 4 | Distribution and Density Functions, Conditional Distributions |
| Week 5 | Asymptotic Approximations for Binomial Random Variables |
| Week 6 | Functions of One Random Variable, Transformation of a Random Variable |
| Week 7 | Mean and Variance Concepts, Moments, Characteristic Functions |
| Week 8 | Midterm Exam |
| Week 9 | Two Random Variables, Bivariate Distributions |
| Week 10 | One Function of Two Random Variables |
| Week 11 | Two Functions of Two Random Variables (Jacobian Matrix) |
| Week 12 | Joint Moments, Joint Characteristic Functions, Conditional Bivariate Distributions |
| Week 13 | Random Processes and their properties, Stationarity, Statistical averages and ergodicity |
| Week 14 | Autocorrelation and cross-correlation functions, Gauss processes |
| Week 15 | Preparation Week for Final Exams |
| Week 16 | Final exam |
Assesment methods
| 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 |
| Midterms | 1 | 50 |
| Final exam | 1 | 50 |
| Total | 100 | |
| Percentage of semester activities contributing grade succes | 0 | 50 |
| Percentage of final exam contributing grade succes | 0 | 50 |
| Total | 100 | |
Workload and ECTS calculation
| Activities | Number | Duration (hour) | Total Work Load |
|---|---|---|---|
| Course Duration (x14) | 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, ect) | 14 | 8 | 112 |
| Presentation / Seminar Preparation | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework assignment | 0 | 0 | 0 |
| Midterms (Study duration) | 1 | 42 | 42 |
| Final Exam (Study duration) | 1 | 44 | 44 |
| Total Workload | 30 | 97 | 240 |
Matrix Of The Course Learning Outcomes Versus Program Outcomes
| D.9. Key Learning Outcomes | Contrubition 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. | X | ||||
| 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. | X | ||||
| 3. Follows and interprets scientific literature and uses them efficiently for the solution of engineering problems. | X | ||||
| 4. Designs and runs research projects, analyzes and interprets the results. | X | ||||
| 5. Designs, plans, and manages high level research projects; leads multidiciplinary projects. | X | ||||
| 6. Produces novel solutions for problems. | X | ||||
| 7. Can analyze and interpret complex or missing data and use this skill in multidiciplinary projects. | X | ||||
| 8. Follows technological developments, improves him/herself , easily adapts to new conditions. | X | ||||
| 9. Is aware of ethical, social and environmental impacts of his/her work. | X | ||||
| 10. Can present his/her ideas and works in written and oral form effectively; uses English effectively | X | ||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest