Erciyes University - Info Package

Course unit title	Level of course unit	Course unit code	Type of course unit	Semester of course unit	Local credit	ECTS credit	Syllabus
ADVANCED PROBABILITY	Third cycle	CENG 515		1	7.50	7.50	Print

Description of course unit

Prerequisites and course requisities	None
Language of instruction	English
Coordinator	Asst. Prof. Özkan Ufuk Nalbantoğlu
Lecturer(s)	Asst. Prof. Özkan Ufuk Nalbantoğlu
Teaching assitant(s)	None
Mode of delivery	Lecture
Course objective	To introduce the basic and advanced concepts of probability and random processes.
Course description	The topics of this course is probability conceprs, Bayes theorem, random variables, law of large numbers, discrete and continious random processes, and basic statistics.

Course contents

1	Experiments, models and probabilities: axiomatic and frequentist approaches.
2	Conditional probability, statistical independence
3	Discrete random variables, probability mass function, cumulative distribution function
4	Expected value, variance, conditional distributions
5	Continuous random variables, probability density function, cumulative distribution function
6	Special probability distribution functions
7	Higher order moments
8	Multivariate probability distributions
9	Joint distributions, expectation and multivariate moments
10	Sum of random variables, moment generators
11	Central limit theorem and apllications
12	Random processes
13	Discrete and continuous Markov processes
14	Random signal theory, detection and estimation
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Learning outcomes of the course unit

1	Learning experiments, models and probabilities,
2	Learning statistical dependence and conditional probabilities.
3	Learning the concepts of discrete and continuous random variables, probability mass, density and cumulative probability functions.
4	Learning the concepts of expectation, variance, and moments.
5	Learning high dimensional probability distributions and random variable-tuples.
6	Learning random processes, law of large numbers and central limit theorem concepts.
7	Learning Markovian processes.
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10

*Contribution level of the course unit to the key learning outcomes

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Number of stars refer to level of contribution from 1 (the least) to 5 (the most)

Planned learning activities, teaching methods and ECTS work load

	Quantity	Time (hour)	Quantity*Time (hour)
Lectures (face to face teaching)	14	3	42
Study hours out of classroom (study before and after the class)	2	5	10
Homework	14	5	70
Presentation / seminar	1	2	2
Quiz	0	0	0
Preparation for midterm exams	1	30	30
Midterm exams	1	1	1
Project (term paper)	0	0	0
Laboratuar	0	0	0
Field study	0	0	0
Preparation for final exam	1	25	25
Final exam	1	3	3
Research	0	0	0
Total work load			183
ECTS			7.50

Assessment methods and criteria

Evaluation during semester	Quantity	Percentage
Midterm exam	1	30
Quiz	0	0
Homework	0	0
Semester total		30
Contribution ratio of evaluation during semester to success		30
Contribution ratio of final exam to success		70
General total		100

Recommended and required reading

Textbook	Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers, by Roy D. Yates and David J. Goodman, 2nd Ed., John Wiley & Sons, Inc.
Additional references	An Introduction to Probability Theory and Its Applications, Volume 1, 3rd Edition William Feller (Princeton Univ., New Jersey), ISBN: 978-0-471-25708-0, 1968. Probability and Random Processes with Applications to Signal Processing, 3/E, by Henry Stark, and John W. Woods, Prentice-Hall, Upper Saddle River, NJ 07458, 2002. Probability and Random Processes for Electrical and Computer Engineers, by J. Gubner, 2006. Probability, Random Variables and Stochastic Processes, A. Papoulis, 3/E, McGraw-Hill Companies, 1991, ISBN-10: 0070484775

Files related to the course unit