COURSE INFORMATION Course Title: FUNDAMENTALS OF PROBABILITY

Code	Course Type	Regular Semester	Theory	Practice	Lab	Credits	ECTS
MTH 207	B	3	2	2	0	3	6

Academic staff member responsible for the design of the course syllabus (name, surname, academic title/scientific degree, email address and signature)	NA
Lecturer (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	Hakan Yozgatlı
Second Lecturer(s) (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	NA
Teaching Assistant(s) and Office Hours:	NA
Language:	English
Compulsory/Elective:	Compulsory
Classroom and Meeting Time:
Course Description:	Fundamentals of Probability course provides a formal and systematic introduction to probability and probabilistic models.
Course Objectives:	The course will introduce the concepts of finite probability theory, continuous probability theory and random processes. Students are expected to gain an understanding and skills in problem solving related to sample spaces, random variables, expectations, transforms, Bernoulli and Poisson processes, finite Markov chains and limit theorems.

COURSE OUTLINE

Week	Topics
1	Introduction to probability.Random experiments, sample spaces and events. Axioms of probability.
2	Conditional probability. Multiplication and total probability rules. Independence. Bayes rule.
3	Discrete random variables. Probability mass function & cumulative distribution functions. Mean and variance.
4	Probability distributions: uniform, binomial and geometric distributions. Their mean and variance.
5	Probability distributions: negative binomial, hypergeometric and Poisson distributions
6	Continuous random variables. Probability density functions and cumulative distribution functions. Mean and variance.
7	Continuous probability distributions. The uniform and normal distribution.
8	Midterm exam
9	The exponential distribution. Overview of lognormal, Erlang, Gamma and Weibull probability distributions.
10	The Bernoulli and Poisson Processes
11	Expectation for Multivariate Distribution
12	The Bernoulli and Poisson Processes
13	Markov Chains
14	Limit theorems

Prerequisite(s):	Calculus I-II, Linear Algebra
Textbook:	D. P. Bertsekas and J. N. Tsitsiklis. «Introduction to Probability», 2nd Ed
Other References:	D. Montgomery, G.Runger «Applied Statistics and Probability for Engineers»
Laboratory Work:
Computer Usage:
Others:	No

COURSE LEARNING OUTCOMES

1	Basic formal elements of probability: random experiments, sample spaces, events
2	Conditional probability and Bayes' rule
3	Discrete and continuous random variables
4	Distributions of functions of random variables
5	Multivariate distributions
6	Fundamental limit theorems

COURSE CONTRIBUTION TO... PROGRAM COMPETENCIES (Blank : no contribution, 1: least contribution ... 5: highest contribution)

No	Program Competencies	Cont.
Bachelor in Computer Engineering (3 years) Program
1	Engineering graduates with sufficient theoretical and practical background for a successful profession and with application skills of fundamental scientific knowledge in the engineering practice.	5
2	Engineering graduates with skills and professional background in describing, formulating, modeling and analyzing the engineering problem, with a consideration for appropriate analytical solutions in all necessary situations	5
3	Engineering graduates with the necessary technical, academic and practical knowledge and application confidence in the design and assessment of machines or mechanical systems or industrial processes with considerations of productivity, feasibility and environmental and social aspects.	4
4	Engineering graduates with the practice of selecting and using appropriate technical and engineering tools in engineering problems, and ability of effective usage of information science technologies.	4
5	Ability of designing and conducting experiments, conduction data acquisition and analysis and making conclusions.	5
6	Ability of identifying the potential resources for information or knowledge regarding a given engineering issue.	3
7	The abilities and performance to participate multi-disciplinary groups together with the effective oral and official communication skills and personal confidence.	4
8	Ability for effective oral and official communication skills in foreign language.	3
9	Engineering graduates with motivation to life-long learning and having known significance of continuous education beyond undergraduate studies for science and technology.	3
10	Engineering graduates with well-structured responsibilities in profession and ethics.	2
11	Engineering graduates who are aware of the importance of safety and healthiness in the project management, workshop environment as well as related legal issues.	4
12	Consciousness for the results and effects of engineering solutions on the society and universe, awareness for the developmental considerations with contemporary problems of humanity.	3

COURSE EVALUATION METHOD

Method	Quantity	Percentage
Homework	3	5
Midterm Exam(s)	1	25
Quiz	2	7.5
Final Exam	1	45
	Total Percent:	100%

ECTS (ALLOCATED BASED ON STUDENT WORKLOAD)

Activities	Quantity	Duration(Hours)	Total Workload(Hours)
Course Duration (Including the exam week: 16x Total course hours)	16	4	64
Hours for off-the-classroom study (Pre-study, practice)	14	3	42
Mid-terms	1	11	11
Assignments	3	5	15
Final examination	1	18	18
Other			0
Total Work Load:			150
Total Work Load/25(h):			6
ECTS Credit of the Course:			6