Course Information


Course Information
Course Title Code Semester L+U Hour Credits ECTS
PROBABILITY AND RANDOM VARIABLES EEE2208 4. Semester 3 + 0 3.0 5.0

Prerequisites None

Language of Instruction English
Course Level Bachelor's Degree
Course Type Compulsory
Mode of delivery
Course Coordinator
Instructors
Assistants
Goals Providing detailed knowledge on probability and random processes to students. Teaching the relation between single/multiple random variable and random processes. Engineering applications of probability theory and random processes.
Course Content Probability concept, randomness, total probability theorem, Bayes' rule, random variables, density and distribution functions, expected value and moments, relation between random variables, statistics, sample mean and variance, experimental distributions, statistical inference, parameter estimation, hypothesis tests, random processes, classification and characterization of random variables, correlation functions, properties of auto-correlation and cross-correlation functions, sample mean and sample correlation functions, raltion between two random processes, power spectral density concept and its properties, white noise, estimation of spectrum, cross-power spectrum, power spectrum in Laplace domain
Learning Outcomes 1) Concept of probability and random processes is known
2) Students achive ability of applying probablity concept to the engineering problems
3) Student can anylze systems by using random processes concept
4) Students can constitute mathematical models
5) Student can make design by using probality and random processes concepts

Weekly Topics (Content)
Week Topics Teaching and Learning Methods and Techniques Study Materials
1. Week Randomness, random signal and systems, probablity and random processes, typical engineering applications. Lecture

 Homework
2. Week Set theory, fundamental concepts in probablity, conditional probality, independent events, total probablity theorem. Lecture

 Homework
3. Week Bayes' rule, combined experiments and Bernoulli experiments, random variable concept, cumulative density function Lecture

 Homework
4. Week Probablity density function, uniform distribution, normal distribution and central limit theorem. Lecture

 Homework
5. Week Expected value and moments (single random variable), condittional distributions, random number generations Lecture

 Homework
6. Week Joint distribution and joint probablity density funtions, independece of random variables. Lecture

 Homework
7. Week Expected value and moments (multipe random variables), relation between two random variables, mean and variance of weighted sum of random variables. Lecture

 Homework
8. Week Joint normal random variables, introduction to statistics, sample mean and variace, experimental distributions. Lecture

 Homework
9. Week Statistical inferece, parameter estimation, hypotesis testing Lecture

 Homework
10. Week Concept of random processes, classification and characterization of random processes. Lecture

 Homework
11. Week Correlation functions, properties of auto-correlation and cross-correlation functions, sample mean and sample correlation funtions. Lecture

 Homework
12. Week Raletion between two random processes, concept of power spectral density and its properties, white noise, estimation of power spectrum. Lecture

 Homework
13. Week Cross-power spectrum, power spectrum in Laplace domain Lecture

 Homework
14. Week Deterministic lineear systems, time domain analysis, frequency domain analysis. Lecture

 Homework

Sources Used in This Course
Recommended Sources
A. Papoulis, S. U. Pillai, “Probability, Random Variables and Stochastic Processes”, McGraw-Hill 2002.
Alberto Leon-Garcia (2008). Probability, Statistics, and Random Processes For Electrical Engineering, 3/E", Prentice Hall,.
D. P. Bertsekas, J. N. Tsitsiklis, “Introduction to Probability, 2nd Edition”, Athena Science 2008ility for Electrical and Computer Engineers, CRC Press.
S. M. Ross, “A First Course In Probability”, Pearson 2009.
X. Rong-Li (1999). Probability, Random Signals and Statistics, CRC Press.

Relations with Education Attainment Program Course Competencies
Program RequirementsContribution LevelDK1DK2DK3DK4DK5
PY1500000
PY2500000
PY3500000
PY4500000

*DK = Course's Contrubution.
0 1 2 3 4 5
Level of contribution None Very Low Low Fair High Very High
.

ECTS credits and course workload
Event Quantity Duration (Hour) Total Workload (Hour)
Course Duration (Total weeks*Hours per week) 14 3
Work Hour outside Classroom (Preparation, strengthening) 5 5
Homework 5 5
Presentation (Including Preparation Time) 5 5
Project (Including Preparation and presentation Time) 2 2
Report (Including Preparation and presentation Time) 2 2
Activity (Web Search, Library Work, Trip, Observation, Interview etc.) 2 2
Practice (Teaching Practice, Music/Musical Instrument Practice , Statistics, Laboratory, Field Work, Clinic and Polyclinic Practice) 1 3
Seminar 1 1
Internship 1 1
Quiz 1 2
Time to prepare for Quiz 1 5
Midterm Exam 1 3
Time to prepare for Midterm Exam 1 5
Final Exam 1 3
Time to prepare for Final Exam 1 5
Total Workload
Total Workload / 30 (s)
ECTS Credit of the Course
Quick Access Hızlı Erişim Genişlet
Course Information
  • Course Information
  • Weekly Topics (Content)
  • Sources Used in This Course
  • Relations with Education Attainment Program Course Competencies
  • ECTS credits and course workload