Introduction to Probability

Prerequisite Background Material (Revision)

Set theory, Counting, Combinatorics, Probability space, Axioms

Lectures

Part I: Introduction to Probability

• Lecture 1: Conditional probabilities and Bayes’ theorem
Slides:
• Pre-lecture presentation style
• Pre-lecture handout style
• Post-lecture handout style
Exercises:
• Ross: Chapter 3.1-3.5
• Dekking: Chapter 3.1-3.4
• PDF file at the end of this page

Part II: Random Variables

• Lecture 2: Random variables, probability mass function, expectation
Slides:
• Pre-lecture presentation style
• Pre-lecture handout style
• Post-lecture handout style
Exercises:
• Ross: Chapter 4.1-4.4
• Dekking: Chapter 4.1-4.2
• PDF file at the end of this page


• Lecture 3: Expectation properties, variance, discrete distributions
Slides:
• Pre-lecture presentation style
• Pre-lecture handout style
• Post-lecture handout style
Exercises:
• Ross: Chapter 4.5-4.6
• Dekking: Chapter 7.1-7.6, 4.3, 4.5-4.6
• PDF file at the end of this page


• Lecture 4: More discrete distributions: Poisson, Geometric, Negative
Slides:
• Pre-lecture presentation style
• Pre-lecture handout style
Exercises:
• Ross: Chapter 4.7-4.8
• Dekking: Chapter 4.4-4.6
• PDF file at the end of this page




Additional Exercises

Some exercises from Ross's book for lectures 1-4: PDF
Some additional exercises: PDF



Solutions to some Exercises can be found under the Supervisors Tab