STAT 559 | Course Introduction and Application Information - Applied Mathematics and Statistics – With Thesis

Course Name

Advanced Probability Theory

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
STAT 559	Fall/Spring	3	0	3	7.5

Prerequisites	None
Course Language	English
Course Type	Elective
Course Level	Second Cycle
Mode of Delivery	-
Teaching Methods and Techniques of the Course	Problem Solving Q&A
National Occupation Classification	-
Course Coordinator	-
Course Lecturer(s)	Prof. Dr. İsmihan Bayramoğlu
Assistant(s)	Arş.Gör. Merve KAHRAMAN ARİMAN

Course Objectives	This course aims to make the students familiar with the basics of Probability Theory, its applications and Statistics.
Learning Outcomes	The students who succeeded in this course; will be able to find probabilities of different events. will be able to work with discrete distribiutions, being able to compute important characteristis for them. will be able to work with continuous distributions and find basic charactheristics for them. will be able to analyze bivariate distributions, compute various characteristics for them. will be able to derive the law, srtong law of large numbers and the central limit theorem for the sums of independent random variables.
Course Description	The axioms of probability theory and historical probability backgrood are discussed. Random events, random variables as well as their basic characteristics are studied. Limit theorems for sums of independent random variables are also considered. Dependent random variables are studied. Bivariate random variables are discussed.
Related Sustainable Development Goals

Course Category	Core Courses
	Major Area Courses
	Supportive Courses
	Media and Management Skills Courses
	Transferable Skill Courses

Week	Subjects	Related Preparation
1	Events. The axioms of probability. Probability space.	“ Probability theory” by A.A. Borovkov:7:27.
2	Random variables and distribution functions.	“ Probability theory” by A.A. Borovkov:38:57.
3	Numerical characteristics of random variables.	“ Probability theory” by A.A. Borovkov:60:92.
4	Bivariate random variables	“A First Course in Probability” by Sheldon Ross, Prentics Hall : 239:269.
5	Bivariate distribution functions.	“A First Course in Probability” by Sheldon Ross, Prentics Hall :270:303.
6	Inequalities.	“A First Course in Probability” by Sheldon Ross, Prentics Hall :400:427.
7	Properties of conditional expectation. Martingales.	“ Probability theory” by A.A. Borovkov:217:246.
8	Midterm Exam
9	Moment generating function and characteristic function.	“ Probability theory” by A.A. Borovkov:92:107.
10	Summation and multiplication of random variables.	“ Probability theory” by A.A. Borovkov:110:115,Pakes, A. G. and Navarro, J. (2007).Distributional characterizations through scaling relations, Australian Journal of Statistics, 49 (2), 115:135.
11	On convergence of random variables and distributions.	“ Probability theory” by A.A. Borovkov:121:134.
12	The central limit theorem and the law of large numbers.	“ Probability theory” by A.A. Borovkov:135:170
13	Limit theorems for dependent random variables.	“Time Series Analysis” by J.D.Hamilton, Princeton, NJ: 180:201.
14	Limit theorems for dependent random variables.	“Time Series Analysis” by J.D.Hamilton, Princeton, NJ: 202:234.
15	Review for Final Exam
16	Review of the Semester

Course Notes/Textbooks	1. “ Probability theory” by A.A. Borovkov
Suggested Readings/Materials	“A First Course in Probability” by Sheldon Ross, Prentice Hall “Time Series Analysis” by J.D.Hamilton, Princeton, NJ.

Semester Activities	Number	Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm	1	50
Final Exam	1	50
Total

Weighting of Semester Activities on the Final Grade	1	50
Weighting of End-of-Semester Activities on the Final Grade	1	50
Total

Semester Activities	Number	Duration (Hours)	Workload
Theoretical Course Hours (Including exam week: 16 x total hours)	16	3	48
Laboratory / Application Hours (Including exam week: '.16.' x total hours)	16		0
Study Hours Out of Class	15	6	90
Field Work			0
Quizzes / Studio Critiques			0
Portfolio			0
Homework / Assignments			0
Presentation / Jury			0
Project			0
Seminar / Workshop			0
Oral Exam			0
Midterms	1	40	40
Final Exam	1	47	47
		Total	225

#

Program Competencies/Outcomes

* Contribution Level

1

2

3

4

5

1

To be able to demonstrate independent and critical thinking in Applied Mathematics and Statistics.

-

X

2

To be able to define problems in Applied Mathematics/Statistics and verify whether they are mathematically/statistically consistent.

-

X

-

3

To be able to analyse and solve real life problems using applied methods and interdisciplinary approach of Mathematics/Statistics.

-

4

To be able to independently conduct, conclude, and report on specialized research in Applied Mathematics and Statistics.

-

X

-

5

To be able to efficiently use national and international resources, for staying updated in the field, communicating with colleagues, and following the related literature.

-

X

-

6

To be able to develop proficiency in using computer software widely utilized in the fields of Applied Mathematics and Statistics.

-

7

To be able to evaluate solution processes efficiently using mathematical reasoning and modeling in order to contribute to the solutions of social and scientific problems.

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8

To be able to synthesize theoretical frameworks with practical applications through mathematical and statistical methods.

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9

To be able to develop strategies, policies and plans for problems and research areas in Applied Mathematics/Statistics in order to interpret the results and translate them into practice.

-

X

-

10

To be able to translate key topics, events, and phenomena in Applied Mathematics and Statistics into the context of other scientific disciplines.

-

11

To be able to engage in lifelong learning by continuously updating and improving knowledge and skills in Applied Mathematics and Statistics.

-

STAT 559 | Course Introduction and Application Information

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

EVALUATION SYSTEM

ECTS / WORKLOAD TABLE

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

IZMIR UNIVERSITY OF ECONOMICS GÜZELBAHÇE CAMPUS

GLOBAL CAREER

CONTRIBUTION TO SCIENCE

VALUING PEOPLE

BENEFIT TO SOCIETY