Undergraduate Level Probability and Statistics Knowledge
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Recommended optional programme components:
None
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Language:
Turkish
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Mode of Delivery:
Face to face
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Course Coordinator:
Prof. Dr. KEMAL FİDANBOYLU
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Course Lecturers:
-
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Contactinformation of the Course Coordinator:
e-posta: kfidan@uludag.edu.tr Uludağ Üniversitesi, Bilgisayar Mühendisliği Bölümü Görükle Kampüsü, 16059 Nilüfer, Bursa
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Website:
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Objective of the Course:
To provide the students with knowledge about basic applications of random processes in engineering, spectral representation, spectral estimation, mean square estimation and entropy.
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Contribution of the Course to Professional Development
Engineering Science: 85%; Engineering Design: 15%
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Learning Outcomes:
1
Discuss random processes and their applications in engineering;
2
Describe random walk, Brownian motion, thermal and shot noise, Poisson points, modulation, cyclostationary and bandlimited processes, sampling theory, bispectra and system identification;
3
Explain spectral representation of random processes;
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Examine ergodicity, spectral and mean square estimation, extrapolation and system identification;
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Analyze Kalman filters;
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Describe maximum entropy method, coding and channel capacity;
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Explain Markov chains;
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Define stationary distributions and limiting probabilities;
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Illustrate Markov processes and queueing theory;
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Course Content:
Week
Theoretical
Practical
1
Random Processes; Definitions; Systems with Stochastic Inputs; The Power Spectrum; Discrete-Time Processes.
2
Random Walks and Other Applications; Random Walks; Poisson Points and Shot Noise; Modulation; Cyclostationary Processes.
3
Bandlimited Processes and Sampling Theory; Deterministic Signals in Noise. Bispectra and System Identification.
4
Spectral Representation; Factorization and Innovations; Finite-Order Systems and State Variables.
5
Fourier Series and Karhunen–Lo`eve Expansions; Spectral Representation of Random Processes.
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Spectrum Estimation; Ergodicity; Extrapolation and System Identification; The General Class of Extrapolating Spectra and Youla’s Parametrization.
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Mean Square Estimation and Filtering.
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Kalman Filters and Their Applications.
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Entropy; Basic Concepts; Random Variables and Stochastic Processes.
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The Maximum Entropy Method; Coding; Channel Capacity.
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Markov Chains; Higher Transition Probabilities and the Chapman–Kolmogorov Equation. Classification of States.
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Stationary Distributions and Limiting Probabilities; Transient States and Absorption Probabilities; Branching Processes.
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Markov Processes and Queueing Theory.
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Networks of Queues.
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Textbooks, References and/or Other Materials:
Athanasios Papoulis and S. Unnikrishna Pillai, "Probability, Random Variables, and Stochastic Processes, 4th Ed., McGraw-Hill, 2002.
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Assesment
TERM LEARNING ACTIVITIES
NUMBER
PERCENT
Midterm Exam
1
20
Quiz
0
0
Homeworks, Performances
1
20
Final Exam
1
60
Total
3
100
Contribution of Term (Year) Learning Activities to Success Grade
40
Contribution of Final Exam to Success Grade
60
Total
100
Measurement and Evaluation Techniques Used in the Course
Classical problem-solving ability will be measured in midterm and final exams. The project will include research, simulation, report writing and presentation on a subject related to the course content.
Information
All exam and project evaluations will be made over 100. It will then be multiplied by the respective contribution percentage and the overall course grade will be obtained out of 100.
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ECTS / WORK LOAD TABLE
Activites
NUMBER
TIME [Hour]
Total WorkLoad [Hour]
Theoretical
14
3
42
Practicals/Labs
0
0
0
Self Study and Preparation
14
5
70
Homeworks, Performances
1
0
0
Projects
1
33
33
Field Studies
0
0
0
Midtermexams
1
15
15
Others
0
0
0
Final Exams
1
20
20
Total WorkLoad
180
Total workload/ 30 hr
6
ECTS Credit of the Course
6
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CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS
