Course Details

ELE 709 Probability Theory and Stochastic Processes
2021-2022 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 ( in real-time and displayed here. Please check the appropriate page on the original site against any technical problems. Course data last updated on 18/05/2022.


Course Name Code Semester Theory
Credit ECTS
Course languageTurkish
Course typeElective 
Mode of DeliveryFace-to-Face 
Learning and teaching strategiesLecture
Question and Answer
Problem Solving
Instructor (s)Department Faculty 
Course objectiveAfter 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
  1. Knows the basic components of probability model.
  2. Knows how to model the sample space in an experiment
  3. Computes the statistical properties (mean, variance, covariance, correlation) of a given one/multi variable random variable(s).
  4. Have the knowledge to follow and understand the advanced and complex probability theory related concepts.
  5. In engineering problems recognizes the random phenomena and applies the correct statistical models.
Course ContentThe 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
ReferencesPapoulis 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

Week 1The Axioms of Probability, Sample Space, Conditional Probability
Week 2Independence, Bernoulli Trials
Week 3Random Variable Concept
Week 4Distribution and Density Functions, Conditional Distributions
Week 5Asymptotic Approximations for Binomial Random Variables
Week 6Functions of One Random Variable, Transformation of a Random Variable
Week 7Mean and Variance Concepts, Moments, Characteristic Functions
Week 8Midterm Exam
Week 9Two Random Variables, Bivariate Distributions
Week 10One Function of Two Random Variables
Week 11Two Functions of Two Random Variables (Jacobian Matrix)
Week 12Joint Moments, Joint Characteristic Functions, Conditional Bivariate Distributions
Week 13Random Processes and their properties, Stationarity, Statistical averages and ergodicity
Week 14Autocorrelation and cross-correlation functions, Gauss processes
Week 15Preparation Week for Final Exams
Week 16Final exam

Assesment methods

Course activitiesNumberPercentage
Field activities00
Specific practical training00
Final exam150
Percentage of semester activities contributing grade succes050
Percentage of final exam contributing grade succes050

Workload and ECTS calculation

Activities Number Duration (hour) Total Work Load
Course Duration (x14) 14 3 42
Laboratory 0 0 0
Specific practical training000
Field activities000
Study Hours Out of Class (Preliminary work, reinforcement, ect)1411154
Presentation / Seminar Preparation000
Homework assignment000
Midterms (Study duration)15050
Final Exam (Study duration) 15454
Total Workload30118300

Matrix Of The Course Learning Outcomes Versus Program Outcomes

D.9. Key Learning OutcomesContrubition level*
1. Has highest level of knowledge in certain areas of Electrical and Electronics Engineering.   X 
2. Has knowledge, skills and and competence to develop novel approaches in science and technology.   X 
3. Follows the scientific literature, and the developments in his/her field, critically analyze, synthesize, interpret and apply them effectively in his/her research.   X 
4. Can independently carry out all stages of a novel research project.   X 
5. Designs, plans and manages novel research projects; can lead multidisiplinary projects.X    
6. Contributes to the science and technology literature.  X  
7. Can present his/her ideas and works in written and oral forms effectively; in Turkish or English.X    
8. Is aware of his/her social responsibilities, evaluates scientific and technological developments with impartiality and ethical responsibility and disseminates them.X    

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

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