STAT 507 | Course Introduction and Application Information - Applied Mathematics and Statistics – With Thesis

Course Name

Advances in Modern Probability and Statistics

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
STAT 507	Fall	0	0	0	7.5

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

Course Objectives	The aim of this course is to enable students to acquire the fundamental concepts of probability theory and statistical inference; to develop their ability to build models and conduct analyses using probability spaces, random variables, basic distributional properties, and reliability measures; and to apply maximum likelihood estimation as well as methods for evaluating the performance of estimators.
Learning Outcomes	The students who succeeded in this course; Formulate probability models using sample spaces, axioms, and core probability properties. Compute conditional probabilities using independence, total probability, and Bayes’ theorem. Explain random variables through their distribution functions, expectations, variances, and transformations. Model discrete, continuous, and multivariate random variables, including sums/convolutions and independence. Analyze lifetime and reliability behavior using hazard rate and mean residual life functions. Construct point estimators, especially maximum likelihood estimators. Apply maximum likelihood estimation (MLE) to regression models. Evaluate estimators using criteria such as bias, variance, efficiency, and consistency.
Course Description	This course covers the fundamental topics of modern probability theory and statistical inference. It addresses probability spaces, random variables (discrete, continuous, and multivariate), expectation, transformations and convolution methods, as well as survival/reliability measures such as the hazard rate and mean residual life. In the statistics component, maximum likelihood estimation, likelihood-based regression, and estimator performance criteria (bias, variance, efficiency, consistency) are examined.
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	Sample space, Classical probability	Sheldon Ross,''A First Course in Probability'' 10th edition,Pearson,2012. ISBN-13: 9780137504589.Chapter 1
2	Axioms of probability, Properties of probability	Sheldon Ross,''A First Course in Probability'' 10th edition,Pearson,2012. ISBN-13: 9780137504589.Chapter 2
3	Conditional probability and independence of events, Total probability formula and Bayes' formula	Sheldon Ross,''A First Course in Probability'' 10th edition,Pearson,2012. ISBN-13: 9780137504589.Chapter 3
4	Random variables and properties of distribution function	Sheldon Ross,''A First Course in Probability'' 10th edition,Pearson,2012. ISBN-13: 9780137504589.Chapter 3
5	Some discrete and continuous random variables, Expectation and variance of a random variable	Sheldon Ross,''A First Course in Probability'' 10th edition,Pearson,2012. ISBN-13: 9780137504589.Chapter 4&5
6	Some discrete and continuous random variables, Expectation and variance of a random variable	Sheldon Ross,''A First Course in Probability'' 10th edition,Pearson,2012. ISBN-13: 9780137504589.Chapter 4&5
7	Expectation and variance of a function of a random variable	Sheldon Ross,''A First Course in Probability'' 10th edition,Pearson,2012. ISBN-13: 9780137504589.Chapter 5
8	Hazard rate functions, mean residual life function	Sheldon Ross,''A First Course in Probability'' 10th edition,Pearson,2012. ISBN-13: 9780137504589.Chapter 5
9	Midterm Exam
10	Multivariate random variables, sum of two random variables and convolution form, Independent random variables	Sheldon Ross,''A First Course in Probability'' 10th edition,Pearson,2012. ISBN-13: 9780137504589.Chapter 6
11	Point estimation, Maximum Likelihood Estimators	G.Casella and R.Berger "Statistical Inference", Cengage Learning, 2nd Edition, 2001. ISBN-13: 978-0534243128. Chapter 7.1-7.2
12	Regression Analysis: Maximum Likelihood Estimators of Regression Parameters	G.Casella and R.Berger "Statistical Inference", Cengage Learning, 2nd Edition, 2001. ISBN-13: 978-0534243128. Chapter 11.3.-12.2.3
13	Methods of Evaluating Estimators	G.Casella and R.Berger "Statistical Inference", Cengage Learning, 2nd Edition, 2001. ISBN-13: 978-0534243128. Chapter 7.3
14	Consistency of Estimators	G.Casella and R.Berger "Statistical Inference", Cengage Learning, 2nd Edition, 2001. ISBN-13: 978-0534243128. Chapter 7.3
15	Semester Review
16	Final Exam

Course Notes/Textbooks

Sheldon Ross,''A First Course in Probability'' 10th edition,Pearson,2012. ISBN-13: 9780137504589

G.Casella and R.Berger "Statistical Inference", Cengage Learning, 2nd Edition, 2001. ISBN-13: 978-0534243128

Suggested Readings/Materials

Shao J. “Mathematical Statistics”, Springer, 2nd Edition, 2003. ISBN-13: 978-0387953823

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	14	6	84
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	53	53
		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.

-

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.

-

8

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

-

X

-

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 507 | 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