MATH401 PROBABILITY THEORY
| Course Code: | 2360401 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 6.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | Lecturer Dr. MUHİDDİN UĞUZ |
| Offered Semester: | Fall Semesters. |
Course Objectives
To introduce and justify principle concepts of probability theory. It presents basic principles of probability theory by providing rigouros proof; constructing of examples; and solving of exercises. Special attention is paid to basic theory of random variables and random processes: laws of large numbers, central limit theorem, Markov chains and limit theorems for them.
Course Content
Events and probability. Combinatorial problems and equally likely events. Probability spaces. Independence and finite product spaces. Random variables and distribution functions. Integration of random variables. Lp - spaces. Convergence of random variables. Conditional expectation. Canonical space of a stochastic process. Markov chains. Martingales.
Course Learning Outcomes
Upon successful completion of this course, a student will be able to:
a) construct appropriate probability spaces;
b) compute probabilities by modeling sample spaces;
c) use basic standard distributions;
d) operate freely with independence, conditional probability, systems of random variables and their moment generating functions;
e) apply probability axioms and rules in probability: Bayes’ theorem, law of total probability, conditional expectation, law of large numbers, and central limit theorem;
f) describe the main properties of probability distributions and random variables;
g) construct discrete Markov chains and investigate their properties by using of limit theorems.
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields. | ✔ | |||
| 2 | Can produce innovative thoughts and products. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Has a comprehension of mathematical symbols, concepts together with the interactions among them and can express his/her solutions similarly. | ✔ | |||
| 5 | Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak). | ✔ | |||
| 6 | Contributes to solving global, environmental and social problems either individually or as being part of a social group. | ✔ | |||
| 7 | Respects ethical values and rules; applies them in professional and social issues. | ✔ | |||
| 8 | Can work cooperatively in a team and also individually. | ✔ | |||
| 9 | Is responsive to life-long learning, improving his/her skills and abilities | ✔ | |||
| 10 | Comprehends necessity of knowledge, can define it and acquires it; uses knowledge effectively and shares it with others | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution