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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 co-requisites: None
Professional practice: No
Purpose of the course: To teach students the advanced topics of probability and mathematical statistics.
   Learning outcomes Up

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

  1. construct a solid background and understanding of the basic results and methods in advanced probability theory and mathematical statistics.

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
    3. Develop mathematical, communicative, problem-solving, brainstorming skills.

    Method of assessment

    1. Written exam
    2. Homework assignment
  2. perceive the weak convergency, convergency with respect to measure and distribution.

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
    3. Develop mathematical, communicative, problem-solving, brainstorming skills.

    Method of assessment

    1. Written exam
  3. apply the methods for obtaining asymptotic distribution of estimation and tests statistics for the relal life problems.

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
    3. Develop mathematical, communicative, problem-solving, brainstorming skills.

    Method of assessment

    1. Written exam
    2. Homework assignment
   Contents Up
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 U-statistics and related estimators. Asymptotic efficiency of estimators.
Week 6: Optimal Test; Randomized test, Strong testler, Neymann-Pearson 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: Radon-Nikodym 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 theorem-finite 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 Up
Method of assessment Week number Weight (%)
Mid-terms: 9 40
Other in-term studies: 0
Project: 0
Homework: 1,2,3,4,5 10
Quiz: 0
Final exam: 16 50
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face 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 mid-term exam: 15 1
Mid-term: 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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