Course Details

ELE709 - Probability Theory and Stochastic Processes

2023-2024 Fall term information
The course is open this term
Name Surname Position Section
Res.Asst.Dr. Gürhan Bulu Supervisor 1
Prof.Dr. Cenk Toker Supervisor 1
Asst.Prof.Dr. Barış Yüksekkaya Supervisor 1
Prof.Dr. Berkan Dülek Supervisor 1
Weekly Schedule by Sections
Section Day, Hours, Place
All sections Friday, 08:40 - 11:30, SS

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.

ELE709 - Probability Theory and Stochastic Processes
Program Theoretıcal hours Practical hours Local credit ECTS credit
PhD 3 0 3 10
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.
Course Outline Weekly
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
Assessment 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
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
Workload and ECTS Calculation
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 11 154
Presentation / Seminar Preparation 0 0 0
Project 0 0 0
Homework assignment 0 0 0
Quiz 0 0 0
Midterms (Study duration) 1 50 50
Final Exam (Study duration) 1 54 54
Total workload 30 118 300
Matrix Of The Course Learning Outcomes Versus Program Outcomes
Key learning outcomes Contribution level
1 2 3 4 5
1. Has highest level of knowledge in certain areas of Electrical and Electronics Engineering.
2. Has knowledge, skills and and competence to develop novel approaches in science and technology.
3. Follows the scientific literature, and the developments in his/her field, critically analyze, synthesize, interpret and apply them effectively in his/her research.
4. Can independently carry out all stages of a novel research project.
5. Designs, plans and manages novel research projects; can lead multidisiplinary projects.
6. Contributes to the science and technology literature.
7. Can present his/her ideas and works in written and oral forms effectively; in Turkish or English.
8. Is aware of his/her social responsibilities, evaluates scientific and technological developments with impartiality and ethical responsibility and disseminates them.
1: Lowest, 2: Low, 3: Average, 4: High, 5: Highest
General Information | Course & Exam Schedules | Real-time Course & Classroom Status
Undergraduate Curriculum | Minor Program For Non-departmental Students | Open Courses, Sections and Supervisors | Weekly Course Schedule | Examination Schedules | Information for Registration | Prerequisite and Concurrent Courses | Legal Info and Documents for Internship | Academic Advisors for Undergraduate Program | Information for ELE 401-402 Graduation Project | Virtual Exhibitions of Graduation Projects | Program Educational Objectives & Student Outcomes | ECTS Course Catalog | HU Registrar's Office
Graduate Curriculum | Open Courses and Supervisors | Weekly Course Schedule | Final Examinations Schedule | Schedule of Graduate Thesis Defences and Seminars | Information for Registration | ECTS Course Catalog - Master's Degree | ECTS Course Catalog - PhD Degree | HU Graduate School of Science and Engineering