# Department of Electrical and Electronics Engineering

Course Details

#### ELE 302 Probability Theory2018-2019 Spring term information

The course is open this term
Place Day Hours Supervisor(s): Dr. Mücahit K. Üner E6 Tuesday 13:00 - 15:45
Place Day Hours Supervisor(s): Dr. Berkan Dülek E3 Tuesday 13:00 - 15:45

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.

ELE302 - PROBABILITY THEORY

Course Name Code Semester Theory
(hours/week)
Application
(hours/week)
Credit ECTS
PROBABILITY THEORY ELE302 6th Semester 3 0 3 5
Prerequisite(s)MAT123 Mathematics I
Course languageEnglish
Course typeMust
Mode of DeliveryFace-to-Face
Learning and teaching strategiesLecture
Problem Solving

Instructor (s)Faculty members
Course objectiveTo 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
1. Know the basic concepts of probability theory.
2. Use common probability distributions and analyse their properties.
3. Compute conditional probability distributions and conditional expectations.
4. Compute distributions by use of transformation techniques and solve problems.
5. Define and use the properties of Stochastic processes, especially Gaussian and Poisson Processes.
Course ContentIntroduction 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

ReferencesPeebles, Jr., Probability, Random Variables, and Random Signal Principles, 4th Ed.,
McGraw-Hill, 2001.

Course outline weekly

WeeksTopics
Week 1Introduction and definitions (Set Theory, Experiment, Sample Space, Events)
Week 2Mathematical model of probability, Joint and conditional probability, Bayes theorem
Week 3Independent events and Bernoulli trials
Week 4The random variable concept
Week 5Probability distribution and density functions, Conditional distributions and densities
Week 6Expected values, moments and characteristic functions
Week 7Transformations of a single random variable
Week 8Midterm
Week 9Multiple random variables, joint distribution and density functions
Week 10Limit theorems, Operations on multiple random variables
Week 11Random processes and their properties
Week 12Independence and stationarity of random processes
Week 13Time averages, statistical averages and ergodicity, Autocorrelation and cross-correlation functions
Week 14Gauss and Poisson processes
Week 15Final exam preparation
Week 16Final exam

Assesment methods

Course activitiesNumberPercentage
Attendance00
Laboratory00
Application00
Field activities00
Specific practical training00
Assignments00
Presentation00
Project00
Seminar00
Midterms140
Final exam160
Total100
Percentage of semester activities contributing grade succes040
Percentage of final exam contributing grade succes060
Total100

Activities Number Duration (hour) Total Work Load
Course Duration (x14) 14 3 42
Laboratory 0 0 0
Application000
Specific practical training000
Field activities000
Study Hours Out of Class (Preliminary work, reinforcement, ect)14570
Presentation / Seminar Preparation000
Project000
Homework assignment000
Midterms (Study duration)11818
Final Exam (Study duration) 12020

Matrix Of The Course Learning Outcomes Versus Program Outcomes

D.9. Key Learning OutcomesContrubition level*
12345
1. PO1. Possesses the theoretical and practical knowledge required in Electrical and Electronics Engineering discipline.    X
2. PO2. Utilizes his/her theoretical and practical knowledge in the fields of mathematics, science and electrical and electronics engineering towards finding engineering solutions.   X
3. PO3. Determines and defines a problem in electrical and electronics engineering, then models and solves it by applying the appropriate analytical or numerical methods.   X
4. PO4. Designs a system under realistic constraints using modern methods and tools.X
5. PO5. Designs and performs an experiment, analyzes and interprets the results.   X
6. PO6. Possesses the necessary qualifications to carry out interdisciplinary work either individually or as a team member.   X
7. PO7. Accesses information, performs literature search, uses databases and other knowledge sources, follows developments in science and technology. X
8. PO8. Performs project planning and time management, plans his/her career development.X
9. PO9. Possesses an advanced level of expertise in computer hardware and software, is proficient in using information and communication technologies.X
10. PO10. Is competent in oral or written communication; has advanced command of English.X
11. PO11. Has an awareness of his/her professional, ethical and social responsibilities.X
12. PO12. Has an awareness of the universal impacts and social consequences of engineering solutions and applications; is well-informed about modern-day problems.X
13. PO13. Is innovative and inquisitive; has a high level of professional self-esteem. X

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