Calendar

Week # lectures recitations key Dates
1 L1: Introduction. Probability, Spaces, and Sigma-Algebras R1  
2

L2: Measures. Carathéodory. Lebesgue Measure and Infinite Coin Flips

L3: Conditioning and Independence. Borel-Cantelli

R2 Homework 1 due
3

L4: Measurable Functions. Random Variables. Cumulative Distribution Functions

L5: Discrete Random Variables

No recitation Homework 2 due
4

L6: Covariance and Correlation. Inclusion-Exclusion Formula, Examples

L7: Abstract Integration

R3 Homework 3 due
5

L8: Monotone and Dominated Convergence Theorems. Fatou's Lemma

L9: Product Measure. Fubini's Theorem

R4 Homework 4 due
6 L10: Continous Random Variables, Examples R5 Homework 5 due
7

L11: Continous Random Variables. Joint Distributions. Conditioning

L12: Derived Distributions

R6 Homework 6 due
8 L13: Transforms. Moment Generating and Characteristic Functions R7  
9

L14: Multivariate Normal

L15: Multivariate Normal. Characteristic Functions

R8 Homework 7 due
10

L16: Convergence of Random Variables

L17: Weak Law of Large Numbers (WLLN) and Central Limit Theorem (CLT)

R9 Homework 8 due
11 L18: Strong Law of Large Numbers (SLLN). Chernoff Bounds R10  
12

L19: Uniform Integrability. Kolmogorov 0–1 Law. Convergence of Series

L20: Stochastic Processes: Bernoulli and Poisson

No recitation Homework 9 due
13

L21: Markov Chains I

L22: Markov Chains II

R11 Homework 10 due
14

L23: Markov Chains III

L24: Markov Chains IV

R12 Homework 11 due
15

L25: Martingales I

L26: Martingales II

No recitation Homework 12 (optional)
16 No lectures. No recitation Final Exam