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
• Post-lecture handout style
Exercises:
• Ross: Chapter 4.7-4.8
• Dekking: Chapter 4.4-4.6
• PDF file at the end of this page


• Lecture 5: Continuous random variables
Slides:
• Pre-lecture presentation style
• Pre-lecture handout style
• Post-lecture handout style
Exercises:
• Ross: Chapter 5.1-5.5
• Dekking: Chapter 5.1-5.3, 5.5, 5.7-5.8
• PDF file at the end of this page


• Lecture 6: Marginals and Joint Distributions
Slides:
• Pre-lecture presentation style
• Pre-lecture handout style
• Post-lecture handout style
Exercises:
• Ross: Chapter 6,7.4
• Dekking: Chapter 9,10
• PDF file at the end of this page


• Lecture 7: Independence, Covariance and Correlation
Slides:
• Pre-lecture presentation style
• Pre-lecture handout style
• Post-lecture handout style
Exercises:
• Ross: Chapter 6,7.4
• Dekking: Chapter 9,10
• PDF file at the end of this page

Part III: Moments and Limit Theorems

• Lecture 8: Basic Inequalities and Law of Large Numbers
Slides:
• Pre-lecture presentation style
• Pre-lecture handout style
• Post-lecture handout style

Exercises:
• Ross: Chapter 8.3
• Dekking: Chapter 14
• PDF file at the end of this page

• Lecture 9: Central Limit Theorem
Slides:
• Pre-lecture presentation style
• Pre-lecture handout style
• Post-lecture handout style

Exercises:
• Ross: Chapter 8.1,8.2
• Dekking: Chapter 13
• PDF file at the end of this page

Part IV: Applications and Statistics

• Lecture 10: Estimators (Part I)
Slides:
• Pre-lecture presentation style
• Pre-lecture handout style
• Post-lecture handout style
Slide 22 was not covered in Lecture 10, but will be covered in Lecture 11

Exercises:
• Dekking: Chapter 17
• PDF file at the end of this page

• Lecture 11: Estimators (Part II)
  
Slides:
• Pre-lecture presentation style
• Pre-lecture handout style
• Post-lecture handout style
Minor correction: on slide 20, N was replaced by k
Exercises:
• Dekking: Chapter 20
• PDF file at the end of this page

• Lecture 12: Online Algorithms
  
Slides:
• Pre-lecture presentation style
• Pre-lecture handout style
• Post-lecture handout style
References:
• ``Sum the odds to one and stop'', F. Thomas Bruss. The Annals of Probability, Volume 28, no 3 (2000), pages 1384-1391.
• ``What is known about Robbins' Problem?''. F. Thomas Bruss. Journal of Applied Probability, Volume 42, no 1 (2005), pages 108-120
Exercises:
• 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