STAT647 Probability Theory
| Course Code: | 2460647 |
| METU Credit (Theoretical-Laboratory hours/week): | 4 (4.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Statistics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Assoc.Prof.Dr. CEREN VARDAR ACAR |
| Offered Semester: | Fall and Spring Semesters. |
Course Objectives
Measure Theoretic Probability Basıc concepts, Sıgma Algebra, Measure, Dynkin`s p-d systems, Measurable functions, Measurable check, Distribution of a random variable, Integration, Expected Value, Radon Nikodym Theorem, Monotone class of functions, Independence, Vector valued random variables, Product measure, Convergence Results, Weak Law of Large Numbers, Strong Law of large numbers, Borel- Cantelli Lemmas, Convergence in distribution, Central Limit Theorem, Point Estimation, Interval Estimation, Hypothesis Testing
Course Content
This is an introductory measure-theoretic probability theory course. We will be covering the fundamental concepts in Statistics to the full extent, such as Law of Large Numbers, Central Limit Theorem, Convergence, Dependence, Independence, Conditional Expectation. The course covers all the content that appear on the Probability Qualification Examination.
Course Learning Outcomes
Measure Theoretic Probability Basıc concepts, Sıgma Algebra, Measure, Dynkin`s p-d systems, Measurable functions, Measurable check, Distribution of a random variable, Integration, Expected Value, Radon Nikodym Theorem, Monotone class of functions, Independence, Vector valued random variables, Product measure, Convergence Results, Weak Law of Large Numbers, Strong Law of large numbers, Borel- Cantelli Lemmas, Convergence in distribution, Central Limit Theorem, Point Estimation, Interval Estimation, Hypothesis Testing