Fundamentals of Probability

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