The calendar below provides information on the course's lecture (L) and recitation (R) sessions.
Course calendar.
| 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
Order Statistics
Bayes Rule
Conjugate Distributions
|
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 |
|