IEM1834 Probability Theory and Mathematical Statistics II

8 ECTS - 4-0 Duration (T+A)- . Semester- 4 National Credit

Information

Code IEM1834
Name Probability Theory and Mathematical Statistics II
Term 2024-2025 Academic Year
Semester . Semester
Duration (T+A) 4-0 (T-A) (17 Week)
ECTS 8 ECTS
National Credit 4 National Credit
Teaching Language Türkçe
Level Doktora Dersi
Type Normal
Mode of study Yüz Yüze Öğretim
Catalog Information Coordinator Prof. Dr. GÜLSEN KIRAL


Course Goal / Objective

The aim of the lesson is to provide a strong foundation in the subjects of advanced probability theory and mathematical statistics.

Course Content

This course covers that Convergence in distribution, weak convergence, characteristic functions, inverse uniqueness theorem, Central Limit Theorem, empirical and asymptotic behavior of order statistics, asymptotic properties of the estimators, the asymptotic behaviour of the test statistics, conditional probability, Martingale, Kolmogorov entity's theorem.

Course Precondition

There are no prerequisites.

Resources

Probability and Statistics for Engineering and Scientists, R.E. Walpole, R.H. Myers, S.L. Myers, K. Ye, Prentice Hall,2007

Notes

Source books, statistical packages


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Defines advanced mathematics and statistics concepts .
LO02 Relates between mathematics and other disciplines.
LO03 Evaluates mathematical models for interdisciplinary problems.
LO04 It expands the abilities of math, statistics, communication, problem solving and brainstorming.
LO05 It exemplifies advanced probability theory and mathematical statistics.


Relation with Program Learning Outcome

Order Type Program Learning Outcomes Level
PLO01 Bilgi - Kuramsal, Olgusal Identify an econometric problem and propose a new solution to it 3
PLO02 Bilgi - Kuramsal, Olgusal Develops new knowledge using current concepts in Econometrics, Statistics and Operations Research 2
PLO03 Bilgi - Kuramsal, Olgusal Explain for what purpose and how econometric methods are applied to other fields and disciplines 2
PLO04 Beceriler - Bilişsel, Uygulamalı Using her knowledge, brings original solutions to problems in Economics, Business Administration and other social sciences
PLO05 Beceriler - Bilişsel, Uygulamalı Creates a new model using mathematics, statistics and econometrics knowledge to solve the problem encountered 2
PLO06 Beceriler - Bilişsel, Uygulamalı Interprets the results obtained from the most appropriate method to predict the model 3
PLO07 Beceriler - Bilişsel, Uygulamalı Performs conceptual analysis to develop solutions to problems 3
PLO08 Beceriler - Bilişsel, Uygulamalı Collects data on purpose 4
PLO09 Beceriler - Bilişsel, Uygulamalı Synthesizes the information obtained by using different sources within the framework of academic rules in a field that does not research 2
PLO10 Beceriler - Bilişsel, Uygulamalı Presents analysis results conveniently 3
PLO11 Beceriler - Bilişsel, Uygulamalı Converts its findings into a master's thesis or a professional report in Turkish or a foreign language
PLO12 Beceriler - Bilişsel, Uygulamalı It researches current approaches and methods to solve the problems it encounters and proposes new solutions 2
PLO13 Beceriler - Bilişsel, Uygulamalı Develops long-term plans and strategies using econometric and statistical methods 1
PLO14 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği Performs self-study using knowledge of Econometrics, Statistics and Operations to solve a problem 3
PLO15 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği Leads the team by taking responsibility 2
PLO16 Yetkinlikler - Öğrenme Yetkinliği Being aware of the necessity of lifelong learning, it constantly renews itself by following the current developments in the field of study 1
PLO17 Yetkinlikler - İletişim ve Sosyal Yetkinlik Uses acquired knowledge in the field to determine the vision, aim, and goals for an organization/institution 2
PLO18 Yetkinlikler - İletişim ve Sosyal Yetkinlik Uses a package program of Econometrics, Statistics, and Operation Research or writes a new code 3
PLO19 Yetkinlikler - İletişim ve Sosyal Yetkinlik Interprets the feelings, thoughts and behaviors of the related persons correctly/expresses himself/herself correctly in written and verbal form 2
PLO20 Yetkinlikler - Alana Özgü Yetkinlik Applies social, scientific and professional ethical values
PLO21 Yetkinlikler - Alana Özgü Yetkinlik Interprets data on economic and social events by following current issues 1


Week Plan

Week Topic Preparation Methods
1 Convergence in distribution, weak convergence. Examining the relevant chapter in the book Öğretim Yöntemleri:
Anlatım
2 Characteristic function, inverse and uniqueness theorems. Examining the relevant chapter in the book Öğretim Yöntemleri:
Anlatım
3 The Central Limit Theorem; Lindenberg and Lyapunov theorem, Feller's theorem. Examining the relevant chapter in the book Öğretim Yöntemleri:
Anlatım
4 Empirical and asymptotic behavior of order statistics Examining the relevant chapter in the book Öğretim Yöntemleri:
Anlatım
5 The asymptotic properties of estimators; asymptotic properties of Maximum likelihood estimators Examining the relevant chapter in the book Öğretim Yöntemleri:
Anlatım
6 Optimal test; powerful tests. Examining the relevant chapter in the book Öğretim Yöntemleri:
Anlatım
7 Neumann-Pearson Lemma. Examining the relevant chapter in the book Öğretim Yöntemleri:
Anlatım
8 Mid-Term Exam Examining the relevant chapter in the book Ölçme Yöntemleri:
Yazılı Sınav
9 Asymptotic behavior of Test statistics. Examining the relevant chapter in the book Öğretim Yöntemleri:
Anlatım
10 Conditional probability; Hann Parse, absolute continuity and Singularity. Examining the relevant chapter in the book Öğretim Yöntemleri:
Anlatım
11 Radon-Nikodym Theorem Examining the relevant chapter in the book Öğretim Yöntemleri:
Anlatım
12 Conditional probability; properties of conditional probability, the conditional probability density function. Examining the relevant chapter in the book Öğretim Yöntemleri:
Anlatım
13 Conditional Expected Value. Examining the relevant chapter in the book Öğretim Yöntemleri:
Anlatım
14 Martingale; Sub-Martingales, The Martingale convergence theorem. Examining the relevant chapter in the book Öğretim Yöntemleri:
Anlatım
15 Kolmogorov entity's theorem-finite dimensional distributions. Examining the relevant chapter in the book Öğretim Yöntemleri:
Anlatım
16 Term Exams Examining the relevant chapter in the book Ölçme Yöntemleri:
Yazılı Sınav
17 Term Exams Examining the relevant chapter in the book Ölçme Yöntemleri:
Yazılı Sınav


Student Workload - ECTS

Works Number Time (Hour) Workload (Hour)
Course Related Works
Class Time (Exam weeks are excluded) 14 4 56
Out of Class Study (Preliminary Work, Practice) 14 8 112
Assesment Related Works
Homeworks, Projects, Others 2 4 8
Mid-term Exams (Written, Oral, etc.) 1 12 12
Final Exam 1 24 24
Total Workload (Hour) 212
Total Workload / 25 (h) 8,48
ECTS 8 ECTS

Update Time: 08.05.2024 11:17