Probability Theory
Syllabus, Bachelor's level, 1MS006
This course has been discontinued.
- Code
- 1MS006
- Education cycle
- First cycle
- Main field(s) of study and in-depth level
- Mathematics G1F
- Grading system
- Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Finalised by
- The Faculty Board of Science and Technology, 30 August 2018
- Responsible department
- Department of Mathematics
Entry requirements
Probability and Statistics, Several Variable Calculus
Learning outcomes
On completion of the course, the student should be able to:
- be able to give an account of the axiomatic foundation of probability theory;
- be able to compute probabilities using combinatorial principles;
- be able to give an account of the concepts of stochastic variable and expected value, and compute probabilities and expected values for given distributions;
- be able to handle conditional probabilities, distributions and expected values;
- know how to use moment generating functions;
- be familiar with applications of the central limit theorem;
- be able to use the Poisson process in stochastic modelling;
- be able to perform computations for simple random walk;
- understand the principles for simulation;
- have a knowledge of probabilistic models in various areas of applications.
Content
Combinatorics. Probability axioms. Calculation of probabilities. Random variables. Probability distributions. Independence and conditional distributions. Expected value and variance, conditional expectations. Moment generating function. Law of large numbers, central limit theory. The Poisson process. Simple random walk. Simulation. Construction of probability models, examples.
Instruction
Lectures and problem solving sessions.
Assessment
Written examination at the end of the course combined with assignments given during the course.
If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.