Department of Electrical and Electronics Engineering

ACADEMICS

Course Details

ELE709 - Probability Theory and Stochastic Processes

2024-2025 Fall term information

The course is open this term

Supervisor(s)
Name Surname	Position	Section
Prof.Dr. Berkan Dülek	Supervisor	1

Weekly Schedule by Sections
Section	Day, Hours, Place
All sections	Tuesday, 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
Key learning outcomes		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

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