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# Probability Theory

2023/2024
Academic Year
ENG
Instruction in English
3
ECTS credits
Course type:
Compulsory course
When:
1 year, 2 module

### Course Syllabus

#### Abstract

The objective of the discipline "Probability Theory" is to lay the foundation of probability for all courses that follow in the “Master of Applied Statistics with Network Analysis” program. The course is strongly related and complementary to other compulsory courses provided in the first year (e.g. Applied Linear Models II, Contemporary Data Analysis) and sets a crucial prerequisite for later courses and research projects as well as for the master thesis.

#### Learning Objectives

• The course gives students an important foundation to develop and conduct their own research as well as to evalu- ate research of others.

#### Expected Learning Outcomes

• Be able to define and apply the concepts of sample space, events, probability, random variables, and their distributions.
• Be able to formulate and apply the definitions of convergence in distribution and in probability, formulate scientific problems involving randomness in mathematical terms.
• Be able to formulate and apply theorems concerning functions of random variables and the moment- generating functions, Chebyshev’s theorem, the Central Limit Theorem and the Law of Large Numbers.
• Be able to use probability in future courses and analytical career overall.
• Have an understanding of the basic principles of probability and lay the foundation for future learning in the area.
• Have the skill to meaningfully develop an appropriate model for the research question, using probability theory.
• Have the skill to work with statistical software, required to analyze the data.
• Know joint probability distributions, expectation, variance and covariance of random variables.
• Know the basic principles of using probability for using analytic models.
• Know the role of probability theory in the sciences, communicate the ideas and results of probability.

#### Course Contents

• Axioms of probability
• Conditional probability and independence
• Discrete Random Variables
• Continuous Random Variables
• Jointly Distributed Random Variables
• Properties of Expectation
• Limit Theorems
• Additional topics in probability

#### Assessment Elements

• Final In-Class and/or Take-home exam (at the discretion of the instructor)
• Class participation
• 3 home assignments

#### Interim Assessment

• 2023/2024 2nd module
0.6 * 3 home assignments + 0.1 * Class participation + 0.3 * Final In-Class and/or Take-home exam (at the discretion of the instructor)

#### Recommended Core Bibliography

• Rohatgi, V. K., & Saleh, A. K. M. E. (2015). An Introduction to Probability and Statistics (Vol. 3rd edition). Hoboken, New Jersey: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1050364
• Venkatesh, S. S. (2013). The Theory of Probability : Explorations and Applications. Cambridge: Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=498312

#### Recommended Additional Bibliography

• Courgeau, D. (2012). Probability and Social Science : Methodological Relationships Between the Two Approaches. Dordrecht: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=523080