## Courses

##### Last Updated:

29/11/2019 - 15:23

## IAM541 - Probability Theory

**Credit: **
3(3-0); **ECTS: **
8.0

**Instructor(s): **
A. Devin Sezer

**Prerequisites: **
Consent of Instructor(s)

#### Course Catalogue Description

Probability spaces. Independence. Conditional probability. Product probability spaces. Random variables and their distributions. Distribution functions. Mathematical expectation (Integration with respect to a probability measure.) Lp-spaces. Moments and generating functions. Conditional expectation. Linear estimation. Gaussian vectors. Various convergence concepts. Central Limit Theorem. Laws of large numbers.#### Course Objectives

The objective of this course is to initiate students to Probability Theory and its applications.#### Course Learning Outcomes

Student who passed this course will- Be able to take courses which build on probability theory (such as the 526 Stochastic Calculus for Finance course in our program)
- Find research material on math finance more mathematically accessible (such as current research papers on math finance or textbooks on the subject). It takes an enormous effort to get used to the technical language that is prevalent today in the field of mathematical finance. After taking this course, the student will find it easier and quicker to master this technical language
- Find it easier to work on research problems in mathematical finance and related fields which use the language of probability theory

#### Tentative (Weekly) Outline

Probability spaces. Independence. Conditional probability. Product probability spaces. Random variables and their distributions. Distribution functions. Mathematical expectation (Integration with respect to a probability measure.) Lp-spaces. Moments and generating functions. Conditional expectation. Linear estimation. Gaussian vectors. Various convergence concepts. Central Limit Theorem. Laws of large numbers.More Info on METU Catalogue

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