Course Name Code Semester T+U Hours Credit ECTS
Probability Theory and Random Variables EEM 586 0 3 + 0 3 6
Precondition Courses
Recommended Optional Courses
Course Language Turkish
Course Level yuksek_lisans
Course Type Optional
Course Coordinator Doç.Dr. GÖKÇEN ÇETİNEL
Course Lecturers
Course Assistants Arş. Gör. Burhan Baraklı
Course Category
Course Objective We usually have to use statistical models in real systems since we can not know, compute, or measure all forces that affect an event. The objective of this course is to teach student how statistical methods are used for analyzing physical systems, especially communication systems.
Course Content Introduction to probability, random variables, functions of random variables, random vectors, expected value, random processes, statistical signal processing applications
# Course Learning Outcomes Teaching Methods Assessment Methods
1 Understanding the concept of a random variable Case Study, Drilland Practice, Demonstration, Simulation, Testing, Homework, Project / Design,
2 Learning computation of a probability density function of a random variable generated from another random variable Simulation, Demonstration, Drilland Practice, Case Study, Homework, Testing, Project / Design,
3 Discussing convergence of random sequences Case Study, Drilland Practice, Demonstration, Simulation, Testing, Homework, Project / Design,
4 Learning random processes Simulation, Demonstration, Drilland Practice, Case Study, Homework, Testing, Project / Design,
5 Investigating statistical signal processing applications of probability Case Study, Drilland Practice, Demonstration, Simulation, Project / Design, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Introduction to probability theory, probability axioms, definitions of conditional and total probability, condition for independence, applications of Bayes theorem
2 Introducing random variable, probability distribution and density functions, examples of discrete and continuous random variables
3 Obtaining probability density function of random variable obtained from another random variable
4 Expected value of a random variable, conditional expected value and moments
5 Chebyshev and Schwartz inequalities, Chernoff bound, moment generating function and characteristic function
6 Joint distribution and density for random vectors, functions of random vectors
7 Expected value vector and covariance matrix for random vectors, properties of covariance matrices, characteristic function computation for random vectors
8 Definition of a random process
9 Some important random processes
10 Computation of probability distribution and density function of a random variable in terms of those of a random variable applied to a linear, time-invariant system
11 Definition of a wide sense stationary random process, vector random processes and state variables representation
12 Estimation of random variables, Kalman and Wiener filtering applications
13 Expectation-maximization algorithm and its applications in signal processing
14 Spectrum estimation
Resources
Course Notes
Course Resources
Order Program Outcomes Level of Contribution
1 2 3 4 5
1 Ability; to Access to wide and deep information with scientific researches in the field of Engineering, evaluate, interpret knowledge and implement. X
1 Ability; to Access to wide and deep information with scientific researches in the field of Engineering, evaluate, interpret knowledge and implement. X
1 Ability; to Access to wide and deep information with scientific researches in the field of Engineering, evaluate, interpret knowledge and implement. X
2 Ability; To complete and implement “Limited or incomplete data” by using the scientific methods. To stick knowledge of different disciplinarians together. X
2 Ability; To complete and implement “Limited or incomplete data” by using the scientific methods. To stick knowledge of different disciplinarians together. X
2 Ability; To complete and implement “Limited or incomplete data” by using the scientific methods. To stick knowledge of different disciplinarians together. X
3 Ability; to consolidate engineering problems, develop proper method to solve and apply innovative solutions. X
3 Ability; to consolidate engineering problems, develop proper method to solve and apply innovative solutions. X
3 Ability; to consolidate engineering problems, develop proper method to solve and apply innovative solutions. X
4 Ability; To develop new and original ideas and methods, To develop new innovative solutions at design of system, component or process X
4 Ability; To develop new and original ideas and methods, To develop new innovative solutions at design of system, component or process X
4 Ability; To develop new and original ideas and methods, To develop new innovative solutions at design of system, component or process X
5 Comprehensive information on modern techniques, methods and their borders which are being applied to engineering. X
5 Comprehensive information on modern techniques, methods and their borders which are being applied to engineering. X
5 Comprehensive information on modern techniques, methods and their borders which are being applied to engineering. X
6 Ability; to design and apply analytical, modeling and experimental based research, analyze and interpret the faced complex issues during the design and apply process. X
6 Ability; to design and apply analytical, modeling and experimental based research, analyze and interpret the faced complex issues during the design and apply process. X
6 Ability; to design and apply analytical, modeling and experimental based research, analyze and interpret the faced complex issues during the design and apply process. X
7 High level ability to define the required information, data and reach, assess. X
7 High level ability to define the required information, data and reach, assess. X
7 High level ability to define the required information, data and reach, assess. X
8 Ability; To lead multi-disciplinary teams To take responsibility to define approaches for complex situations. X
8 Ability; To lead multi-disciplinary teams To take responsibility to define approaches for complex situations. X
8 Ability; To lead multi-disciplinary teams To take responsibility to define approaches for complex situations. X
9 Systematic and clear verbal or written transfer of the process and results of studies at national and international environments X
9 Systematic and clear verbal or written transfer of the process and results of studies at national and international environments X
9 Systematic and clear verbal or written transfer of the process and results of studies at national and international environments X
10 Social, scientific and ethical values guarding adequacy at all professional activities and at the stage of data collection, interpretation, announcement. X
10 Social, scientific and ethical values guarding adequacy at all professional activities and at the stage of data collection, interpretation, announcement. X
10 Social, scientific and ethical values guarding adequacy at all professional activities and at the stage of data collection, interpretation, announcement. X
11 Awareness at new and developing application of profession and ability to analyze and study on those applications. X
11 Awareness at new and developing application of profession and ability to analyze and study on those applications. X
11 Awareness at new and developing application of profession and ability to analyze and study on those applications. X
12 Ability to interpret engineering application’s social and environmental dimensions and it’s compliance with the social environment. X
12 Ability to interpret engineering application’s social and environmental dimensions and it’s compliance with the social environment. X
12 Ability to interpret engineering application’s social and environmental dimensions and it’s compliance with the social environment. X
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 30
1. Ödev 3
1. Performans Görevi (Laboratuvar) 20
1. Performans Görevi (Seminer) 20
2. Ödev 3
3. Ödev 3
4. Ödev 3
5. Ödev 3
6. Ödev 3
7. Ödev 3
8. Ödev 3
9. Ödev 3
10. Ödev 3
Total 100
1. Yıl İçinin Başarıya 60
1. Final 40
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 2 32
Mid-terms 10 7 70
Quiz 1 5 5
Assignment 1 10 10
Oral Examination 1 10 10
Performance Task (Laboratory) 1 15 15
Total Workload 190
Total Workload / 25 (Hours) 7.6
dersAKTSKredisi 6