| SES # | TOPICS | KEY DATES |
|---|---|---|
| L1 | Introduction Probability Spaces | |
| R1 | Background Material from Analysis | Problem set 1 out |
| L2 | Probability Measure, Lebesgue Measure | |
| L3 | Conditioning, Bayes Rule, Independence, Borel-Cantelli-Lemmas | |
| R2 | Measurability Borel-Cantelli | Problem set 1 due |
| L4 | Counting | Problem set 2 out |
| R3 | Counting Exercises | |
| L5 | Measurable Functions, Random Variables, Cumulative Distribution Functions | |
| L6 | Discrete Random Variables, Expectation | Problem set 2 due |
| R4 | Inclusion-exclusion Principle Pointwise Limit of Functions Random Variables | Problem set 3 out |
| L7 | Covariance and Correlation Inclusion-exclusion Principle | |
| L8 | Continuous Random Variables, Expectation | |
| R5 | Independence of RVs Continuous RV Sampling | Problem set 3 due |
| L9 | Continuous Random Variables, Joint Distributions, Bayes Rule | |
| R6 | Expectation | Problem set 4 out |
| L10 | Derived Distributions | |
| L11 | Abstract Integration | |
| R7 | Midterm Review | Problem set 4 due |
| L12 | Monotone and Dominated Convergence Fatou's Lemma | |
| Midterm Exam | ||
| L13 | Product Measure, Fubini Theorem Abstract Definition of Conditional Expectation | Problem set 5 out |
| R8 | Fubini's Theorem | |
| L14 | Transforms: Moment Generating and Characteristic Functions | Problem set 5 due |
| L15 | Multivariate Normal | |
| R9 | Continuity of the Characteristic Function Variance of Random Sum of Random Variables Sum of a Geometric Number of Exponential Random Variables Gaussian Random Vector Bayes Rule | |
| L16 | Multivariate Normal (cont.) | Problem set 6 out |
| L17 | Weak Law of Large Numbers Central Limit Theorem | Problem set 6 due Problem set 7 out |
| L18 | Bernoulli and Poisson Processes | |
| L19 | Poisson Process (cont.) | Problem set 8 out |
| R10 | Finite-state Markov Chains Convergence of Random Variables | Problem set 7 due |
| L20 | Finite-state Markov Chains | |
| L21 | Finite-state Markov Chains (cont.) | Problem set 8 due Problem set 9 out |
| L22 | Finite-state Markov Chains (cont.) | |
| L23 | Convergence of Random Variables (cont.) | |
| R11 | Bernoulli and Poisson Processes | Problem set 9 due Problem set 10 out |
| L24 | Strong Law of Large Numbers | |
| L25 | L2 Theory of Random Variables Construction of Conditional Expectations | |
| L26 | Miscellaneous Theoretical Topics | Problem set 10 due |
| L27 | Large Deviations (Guest Lecture) | |
| Review Session | ||
| Final Exam |