# Department of Electrical and Electronics Engineering

Course Details

#### ELE302 - Probability Theory

2023-2024 Fall term information
The course is not open this term
ELE302 - Probability Theory
 Program Theoret�cal hours Practical hours Local credit ECTS credit Undergraduate 3 0 3 5
 Obligation : Must Prerequisite courses : - 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 To have the students acquire the skills to analyze nondeterministic signals by modelling them as random processes. Learning outcomes : Know the basic concepts of probability theory. Use common probability distributions and analyse their properties. Compute conditional probability distributions and conditional expectations. Compute distributions by use of transformation techniques and solve problems. Define and use the properties of Stochastic processes, especially Gaussian and Poisson Processes. 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 Definition of a random process Independence and stationarity Time averages, statistical averages and ergodicity Autocorrelation and cross-correlation functions Gauss and Poisson processes References : 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 concept
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 Random processes and their properties
12 Independence and stationarity of random processes
13 Time averages, statistical averages and ergodicity, Autocorrelation and cross-correlation functions
14 Gauss and Poisson processes
15 Final exam preparation
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 40
Final exam 1 60
Total 100
Percentage of semester activities contributing grade success 40
Percentage of final exam contributing grade success 60
Total 100
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 5 70
Presentation / Seminar Preparation 0 0 0
Project 0 0 0
Homework assignment 0 0 0
Quiz 0 0 0
Midterms (Study Duration) 1 18 18
Final Exam (Study duration) 1 20 20
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.
1: Lowest, 2: Low, 3: Average, 4: High, 5: Highest