Probability Theory

5 credits

Syllabus, Bachelor's level, 1MS006

This course has been discontinued.

A revised version of the syllabus is available.

Code: 1MS006
Education cycle: First cycle
Main field(s) of study and in-depth level: Mathematics G1F
Grading system: Pass with distinction (5), Pass with credit (4), Pass (3), Fail (U)
Finalised by: The Faculty Board of Science and Technology, 15 March 2007
Responsible department: Department of Mathematics

What is a course syllabus?

Entry requirements

Probability and Statistics, Several Variable Calculus

Learning outcomes

In order to pass the course (grade 3) the student should

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. Moreover, compulsory assignments may be given during the course.