PhD in Mechatronic Engineering (English) with a bachelor's degree
PhD	TR-NQF-HE: Level 8	QF-EHEA: Third Cycle	EQF-LLL: Level 8

General course introduction information

Course Code:

ECE535

Course Name:

Random Processes and Estimation

Course Semester:

Fall

Course Credits:

Theoretical	Practical	Credit	ECTS
		3	10

Language of instruction:

Course Requisites:

Does the Course Require Work Experience?:

Type of course:

Department Elective

Course Level:

PhD

TR-NQF-HE:8. Master`s Degree

QF-EHEA:Third Cycle

EQF-LLL:8. Master`s Degree

Mode of Delivery:

Face to face

Course Coordinator :

Dr.Öğr.Üyesi DİDEM KIVANÇ TÜRELİ

Course Lecturer(s):

Course Assistants:

Course Objective and Content

Course Objectives:

The aim of the course is to gain basic knowledge and abilities to the students about Combinatorial methods; product rule, permutation, combination. Probability; probability axioms, conditional probability, Bayes formula. Random variable; distribution function, probability function, Chebyshev inequality. Discrete and continuous distributions; uniform, Bernoulli, Poisson, geometric, hypergeometric, normal, exponential, gamma and beta distributions. Generating functions.

Course Content:

Combinatorial methods; product rule, permutation, combination. Probability; probability axioms, conditional probability, Bayes formula. Random variable; distribution function, probability function, Chebyshev inequality. Discrete and continuous distributions; uniform, Bernoulli, Poisson, geometric, hypergeometric, normal, exponential, gamma and beta distributions. Generating functions.

Learning Outcomes

The students who have succeeded in this course;

Learning Outcomes

1 - Knowledge
Theoretical - Conceptual
1) Solve engineering problems using probability theory.
2) Solve engineering problems using random processes.
3) Formulate random theory based models of real life problems.
2 - Skills
Cognitive - Practical
3 - Competences
Communication and Social Competence
Learning Competence
Field Specific Competence
Competence to Work Independently and Take Responsibility

Lesson Plan

Week	Subject	Related Preparation
1)	Discrete Random Variables Continuous & General Random Variables	Read the relevant section of the textbook.
2)	Random Vectors Function of Random Variables Expectation, Variance, Conditional Expectation	Read the relevant section of the textbook.
3)	Bounds: Jensen, Markov, Chebyshev, Chernoff Law of Large Numbers, Central Limit Theorem Random Graphs	Read the relevant section of the textbook.
4)	Mini-Lab: Introduction to Python, Phase Transitions in Random Graphs, Auctions	Read the relevant section of the textbook.
5)	Discrete-Time Markov Chains (e.g., PageRank) Law of Large Numbers for Markov Chains	Read the relevant section of the textbook.
6)	Poisson Process	Read the relevant section of the textbook.
7)	Continuous-Time Markov Chains & Queues	Read the relevant section of the textbook.
8)	Mini-Lab & Project: Search Engines (PageRank), Digital Communication, Markov Decision Processes (e.g., Settlers of Catan)	Read the relevant section of the textbook.
9)	Statistical Inference Hypothesis Testing	Read the relevant section of the textbook.
10)	Maximum Likelihood Estimation	Read the relevant section of the textbook.
11)	Bayesian Inference	Read the relevant section of the textbook.
12)	Confidence Intervals	Read the relevant section of the textbook.
13)	Mini-Lab & Project: Real-world applications (e.g., Signal Processing, Communication Systems)	Read the relevant section of the textbook.
14)	Review	Review

Sources

Course Notes / Textbooks:	Probability and Statistics for Engineers and Scientists, Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, Keying Ye, Pearson Ed. ISBN 13: 978-0-321-62911-1
References:	Lecture Notes- Ders notları

Course-Program Learning Outcome Relationship

Learning Outcomes	1	2	3
Program Outcomes
1) Knowledge and ability to apply the interdisciplinary synergetic approach of mechatronics to the solution of engineering problems
2) Ability to design mechatronic products and systems using the mechatronics approach
3) Knowledge and ability to analyze and develop existing products or processes with a mechatronics approach
4) Ability to communicate effectively and teamwork with other disciplines
5) Understanding of performing engineering in accordance with ethical principles
6) Understanding of using technology with awareness of local and global socioeconomic impacts
7) Approach to knowing and fulfilling the necessity of lifelong learning

Course - Learning Outcome Relationship

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

	Program Outcomes	Level of Contribution
1)	Knowledge and ability to apply the interdisciplinary synergetic approach of mechatronics to the solution of engineering problems
2)	Ability to design mechatronic products and systems using the mechatronics approach
3)	Knowledge and ability to analyze and develop existing products or processes with a mechatronics approach
4)	Ability to communicate effectively and teamwork with other disciplines
5)	Understanding of performing engineering in accordance with ethical principles
6)	Understanding of using technology with awareness of local and global socioeconomic impacts
7)	Approach to knowing and fulfilling the necessity of lifelong learning

Learning Activity and Teaching Methods

Lesson
Reading
Problem Solving
Q&A / Discussion

Assessment & Grading Methods and Criteria

Written Exam (Open-ended questions, multiple choice, true-false, matching, fill in the blanks, sequencing)

Assessment & Grading

Semester Requirements	Number of Activities	Level of Contribution
Midterms	2	% 50
Final	1	% 50
total		% 100
PERCENTAGE OF SEMESTER WORK		% 50
PERCENTAGE OF FINAL WORK		% 50
total		% 100

Workload and ECTS Credit Grading

Activities	Number of Activities	Duration (Hours)	Workload
Course Hours	15	3	45
Study Hours Out of Class	15	3	45
Midterms	2	15	30
Final	1	20	20
Total Workload			140