Department of Computer Science and Technology

Introduction to Probability

# Introduction to Probability

For a discussion forum, please go to the course Moodle page.

Fri 30 April at 10am: Link to live online brief Welcome meeting

## Lectures

### Part I: Introduction to Probability

• Lecture 1/2: Introduction, Counting, Combinatorics, Probability space, Axioms
• Slides: Recordings: Exercises:
• Ross: Chapter 1, Chapter 2.1-2.5
• Dekking: Chapter 2.1-2.5

• Lecture 2/3: Conditional probabilities and Bayes’ theorem
• Slides: Recordings: Exercises:
• Ross: Chapter 3.1-3.5
• Dekking: Chapter 3.1-3.4

### Part II: Random Variables

• Lecture 3: Random variables, probability mass function, expectation
• Slides: Recordings: Exercises:
• Ross: Chapter 4.1-4.4
• Dekking: Chapter 4.1-4.2

• Lecture 4: Expectation properties, variance, discrete distributions
• Slides: Recordings: Exercises:
• Ross: Chapter 4.5-4.6
• Dekking: Chapter 7.1-7.6, 4.3, 4.5-4.6

• Lecture 5: More discrete distributions: Poisson, Geometric, Negative
• Slides: Recordings: Exercises:
• Ross: Chapter 4.7-4.8
• Dekking: Chapter 4.4-4.6

• Lecture 6: Continuous random variables
• Slides: Recordings: Exercises:
• Ross: Chapter 5.1-5.5
• Dekking: Chapter 5.1-5.3, 5.5, 5.7-5.8

• Lecture 7: Marginals and Joint Distributions, Independence, Covariance and Correlation
• Slides: Recordings: Exercises:
• Ross: Chapter 6,7.4
• Dekking: Chapter 9,10

### Part III: Moments and Limit Theorems

• Lectures 8 & 9: Markov, Chebyshev, Weak Law of Large Numbers, Central Limit Theorem
• Slides: Recordings: Exercises:
• Ross: Chapter 8
• Dekking: Chapter 13,14

### Part IV: Applications and Statistics

• Lecture 10: Statistics and Estimators
• Slides:
• Update: on slide 19, first line: +X_n has been replaced by -X_n. Thanks to Saksham Shah for spotting this!
• Update: the explanations on slide 20 have been expanded (it is important that T(X) is not the constant zero polynomial.) Thanks to an anynomous student for spotting this
Recordings: Exercises:
• Dekking: Chapter 17.1-17.2,19,20

• Lecture 11: Testing Probability Distributions (this part is non-examinable)
• Slides: Recordings: Exercises:

• Lecture 12: Online Algorithms (Decision Making Under Uncertainty)
• Slides:
Update: In Slide 14 the s/(s-1)-terms have been replaced by (s-1)/s. Thanks to an anonymous student for spotting this!
Recordings:
• Introduction (video recording)
• The (Original) Secretary Problem Part One: Definition, Illustration, Basic Strategies (video recording)
• The (Original) Secretary Problem Part Two: Optimal Strategy (video recording)
• The Secretary Problem with Payoff Definition, Conclusions (video recording)
• The Odd's Algorithm, Application of Odd's Algorithm to the Original Secretary Problem (video recording)
Exercises: