Syllabus ( MATH 582 )

Basic information


Course title: 
Probability And Mathematical Statistics II 
Course code: 
MATH 582 
Lecturer: 
Prof. Dr. Nuri ÇELİK

ECTS credits: 
7.5 
GTU credits: 
3 (3+0+0) 
Year, Semester: 
1/2, Fall and Spring 
Level of course: 
Second Cycle (Master's) 
Type of course: 
Area Elective

Language of instruction: 
English

Mode of delivery: 
Face to face , Group study

Pre and corequisites: 
None 
Professional practice: 
No 
Purpose of the course: 
To teach students the advanced topics of probability and mathematical statistics. 



Learning outcomes


Upon successful completion of this course, students will be able to:

construct a solid background and understanding of the basic results and methods in advanced probability theory and mathematical statistics.
Contribution to Program Outcomes

Define and manipulate advanced concepts of Mathematics

Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems

Develop mathematical, communicative, problemsolving, brainstorming skills.
Method of assessment

Written exam

Homework assignment

perceive the weak convergency, convergency with respect to measure and distribution.
Contribution to Program Outcomes

Define and manipulate advanced concepts of Mathematics

Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems

Develop mathematical, communicative, problemsolving, brainstorming skills.
Method of assessment

Written exam

apply the methods for obtaining asymptotic distribution of estimation and tests statistics for the relal life problems.
Contribution to Program Outcomes

Define and manipulate advanced concepts of Mathematics

Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems

Develop mathematical, communicative, problemsolving, brainstorming skills.
Method of assessment

Written exam

Homework assignment


Contents


Week 1: 
Convergency of Distributions; Weak convergency, 
Week 2: 
Characteristic functions; inversion and the Uniqness theorem. 
Week 3: 
Centeral limit theorem; Lindeberg and Lyapounov Theorems, Feller's theorem, Limit theorem in R^k. 
Week 4: 
Large sample behavior of emprical distributions and order statistics. 
Week 5: 
Asymptotic behavior of Estimators; Asymptotic behavior of Maximum likelihood estimators, Asymptotic behavior of Ustatistics and related estimators. Asymptotic efficiency of estimators.

Week 6: 
Optimal Test; Randomized test, Strong testler, NeymannPearson Lemma. 
Week 7: 
Asymptotic behavior of Test statistics

Week 8: 
Conditional Probability; Additive set function, Hann Decomposition, Absolute continuity and Singularity. 
Week 9: 
Midterm exam; 
Week 10: 
RadonNikodym Theorem 
Week 11: 
Conditional Probability; Properties of conditional probability, Conditional probability distribution. 
Week 12: 
Conditional expectations 
Week 13: 
Martingales; submartingales, function of martingales. 
Week 14: 
martingale convergence theorems, Applications to Likelihood ratio test, bayesestimation. 
Week 15*: 
Kolmogorov's existance theoremfinite dimensional distribıtions 
Week 16*: 
Final exam 
Textbooks and materials: 
Probability and measure by Patrick Bilingsley Statistical Inference, by Casella and Berger,

Recommended readings: 
Arnold, S. F. Mathematical Statistics, Prentice HallI Introduction to Mathematical Statistics by Hogg and Craig Introduction to Probability Models by Ross


* Between 15th and 16th weeks is there a free week for students to prepare for final exam.




Assessment



Method of assessment 
Week number 
Weight (%) 

Midterms: 
9 
40 
Other interm studies: 

0 
Project: 

0 
Homework: 
1,2,3,4,5 
10 
Quiz: 

0 
Final exam: 
16 
50 

Total weight: 
(%) 



Workload



Activity 
Duration (Hours per week) 
Total number of weeks 
Total hours in term 

Courses (Facetoface teaching): 
3 
14 

Own studies outside class: 
4 
14 

Practice, Recitation: 
0 
0 

Homework: 
10 
5 

Term project: 
0 
0 

Term project presentation: 
0 
0 

Quiz: 
0 
0 

Own study for midterm exam: 
15 
1 

Midterm: 
1 
1 

Personal studies for final exam: 
20 
1 

Final exam: 
2 
1 



Total workload: 



Total ECTS credits: 
* 

* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)



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