Course pages 2019–20
Introduction to Probability
Lectures
Part I: Introduction to Probability
- Lecture 1/2: Introduction, Counting, Combinatorics, Probability space, Axioms
- Motivation, set theory revision (video recording)
- Counting (video recording)
- Combinatorics: permutations, combinations (video recording)
- Probability space, axioms, union bound (video recording)
- Ross: Chapter 1, Chapter 2.1-2.5
- Dekking: Chapter 2.1-2.5
- Lecture 2/3: Conditional probabilities and Bayes’ theorem
- Conditional probability (video recording)
- Bayes' theorem (video recording)
- Independence (video recording)
- Ross: Chapter 3.1-3.5
- Dekking: Chapter 3.1-3.4
Part II: Random Variables
- Lecture 3: Random variables, probability mass function, expectation
- Random variable (video recording)
- Probability mass function (video recording)
- Cumulative distribution function (video recording)
- Expectation (video recording)
- Ross: Chapter 4.1-4.4
- Dekking: Chapter 4.1-4.2
- Lecture 4: Expectation properties, variance, discrete distributions
- Properties of expectation (video recording)
- Variance (video recording)
- Bernoulli discrete random variable, Binomial discrete random variable (video recording)
- 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
- Poisson discrete random variable (video recording)
- Geometric discrete random variable (video recording)
- Negative binomial discrete random variable, Hypergeometric discrete random variable (video recording)
- Ross: Chapter 4.7-4.8
- Dekking: Chapter 4.4-4.6
- Lecture 6: Continuous random variables
- Pre-lecture presentation style (updated)
- Pre-lecture handout style (updated)
- Post-lecture handout style (updated)
- Continuous random variables (video recording) (updated)
- Cumulative distribution functions, expectation, variance (video recording)
- Uniform random variable, Exponential random variable (video recording)
- Normal (Gaussian) random variable (video recording)
- 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
- Introduction to Lectures 7-12 (video recording)
- Joint Distribution, Marginal Distribution (discrete) (video recording)
- Joint Distribution, Marginal Distribution (continuous), Independence (video recording)
- Covariance, Correlation Coefficient (video recording)
- 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 & 9: Markov, Chebyshev, Weak Law of Large Numbers, Central Limit Theorem
- Introduction and Warm-up Example (video recording)
- Markov's inequality, Cheyshev's inequality (video recording)
- Weak Law of Large Numbers (video recording)
- Central Limit Theorem, Illustrations (video recording)
- Applications of the Central Limit Theorem, Cauchy Distribution Example (video recording)
- Bonus Material (non-examinable): Introduction to Moments and a Proof Sketch of the Central Limit Theorem (video recording)
- Ross: Chapter 8
- Dekking: Chapter 13,14
- PDF file at the end of this page
Part IV: Applications and Statistics
- Lecture 10: Statistics and Estimators
- Introduction (video recording)
- Empirical Distribution, Definition of Estimator (video recording)
- Examples of Estimators, Definition of Bias (video recording)
- Analysis of Bias, Estimator for Expectaton and Variance, Non-Existence of Unbiased Estimator (video recording)
- Estimating Population Size, Mean Squared Error (video recording)
- Examples of Mean Squared Error for different Estimators (video recording)
- Dekking: Chapter 17.1-17.2,19,20
- PDF file at the end of this page
- Lecture 11: Testing Probability Distributions
- Introduction (video recording)
- Testing Uniformity (Part One): Motivation and Problem Definition (video recording)
- Testing Uniformity (Part Two): Algorithm and Analysis (video recording)
- Conclusion (video recording)
- PDF file at the end of this page
- Lecture 12: Online Algorithms (Decision Making Under Uncertainty)
- 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)
- PDF file at the end of this page
- New: Concluding remarks
- Well done, good luck and see you soon, hopefully! (video recording)
New: Solutions to some Exercises can be found under the Supervisors Tab