Syllabus ( MATH 581 )
Basic information  
Course title:  Probability And Mathematical Statistics I  
Course code:  MATH 581  
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  
Pre and corequisites:  None  
Professional practice:  No  
Purpose of the course:  The main goal of this course is to introduce the students to advence probability theory and mathematical statistics and encourage them to do research on paremeter estimation and hypothesis testing  
Learning outcomes  
Upon successful completion of this course, students will be able to:

explain fundamental concept of the advance 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
 Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
 Develop mathematical, communicative, problemsolving, brainstorming skills.
Method of assessment
 Written exam

demostrate how to construct the extension and check the uniqness.
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

explain the concept of Measures; General measures, Outher measures, Maesure in Euclidean Space.
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

explain the properties of integral and integral with respect to Lebesgue measure.
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

demostrate the Product Measure and Fubini Theorem.
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

demostrate the characterization of Exponential distribution, and relate to poisson process
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
 Homework assignment

percieve the principles of data reduction and relate this to point estimation
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
 Homework assignment
Assessment  
Method of assessment  Week number  Weight (%) 
Midterms:  10  30 
Other interm studies:  0  
Project:  0  
Homework:  1,2,3,4,5,6,7  20 
Quiz:  0  
Final exam:  16  50 
Total weight:  (%) 
