Foundations of Probability (Autumn 2024)

Abstract

The course gives an in-depth introduction to fundamental principles of probability theory.

Description

The scope of this course is twofold. First and foremost, the course gives an in-depth introduction to fundamental principles of probability theory. Secondly, via a careful discussion of probabilistic concepts and results the student will be introduced also to mathematical thinking and obtain a fluency in reading, deriving, and communicating mathematical results.

Topics include

• Probabilities.
• Random variables and their distributions
• Joint and marginal distributions.
  
• Expectation and variance.
• Transformations of random variables.
• Discrete and continuous distributions
• Statistical independence.
• Conditional probability and Bayes’ theorem.

Formal prerequisites

Students are expected to fulfill the admission requirements for the BSc in Data Science.

Intended learning outcomes

After the course, the student should be able to:

• Define basic concepts in probability.
• Identify relevant random variables to describe an experiment and relate to standard families of distributions.
• Compute probabilities and conditional probabilities from basic definitions and principles.
• Derive the expectation and variance of a random variable.
• Apply classical results from probability theory to reason about the distribution of a transformation of a random variable
• Formulate or derive a mathematical result and argue for its correctness using appropriate mathematical terminology.

Ordinary exam

Exam type:
A: Written exam on premises, External (7-point scale)
Exam variation:
A33: Written exam on premises on paper with restrictions