STAT602 ADVANCED PROBABILITY THEORY II
| Course Code: | 2460602 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Statistics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Prof.Dr. AYŞEN AKKAYA |
| Offered Semester: | Fall Semesters. |
Course Objectives
This is the second part of a two semester doctoral course sequence. It covers conditional expectation, martingales, infinite divisibility, limit distributions, Brownian motion. These two-semester sequence courses cover all of the topics that will appear on the Probability Preliminary Examination.
Course Content
Concept of conditioning. From independence to dependence. Ergodic theorems. Martingales and decomposability. Brownian motion and limit distributions.
Course Learning Outcomes
Convergence in distribution and Limiting theorems. Concept of conditioning. Martingales and decomposability. Brownian motion and limit distributions.
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Ability for converting theoretical, methodological, and computational statistical knowledge into analytical solutions in researches requiring statistical analyses. | ✔ | |||
| 2 | Ability for specifiying problems in real life situations bearing uncertainty, forming hypotheses, modeling, application, and interpreting the results. | ✔ | |||
| 3 | Ability for using current technology, computer softwares for statistical applications, computer programming for specific problems when necessary, writing computer codes for speeding up statistical calculations, organizing and cleaning databases, and preparing them for statistical analyses, and data mining. | ✔ | |||
| 4 | Ability for taking part in intra/inter disciplinary team work, efficient use of time, taking responsibility as a team leader, and entrepreneurship. | ✔ | |||
| 5 | Ability for taking responsibility in solitary work and producing creative solutions. | ✔ | |||
| 6 | Ability for keeping up-to-date with current advancements in statistical sciences, doing research, being open-minded, and adopting critical thinking. | ✔ | |||
| 7 | Ability for effective communication both in Turkish and English in specification of statistical problems, analyes, and interpretation of findings. | ✔ | |||
| 8 | Ability for using the knowledge in the field of expertise for the welfare of the society. | ✔ | |||
| 9 | Ability for suggesting the researchers in a comprehensible way the appropriate statistical methods for problems in fields that use statistics such as economics, finance, industrial engineering, genetics, and medicine and apply if needed. | ✔ | |||
| 10 | Ability for catalyzing discussions and presentations, public speaking, making presentations, communicating topics of expertise to the audiance in a comprehensible way. | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution