Text Patrick Billingsley, Probability and Measure
| Section | Problems | Due |
| 2. Probability measures | 2.3, 2.4 , 2.6, 2.15, 2.17, 2.19 | Sept. 7 |
| 2. Probability measures | 2.14, 2.20 | Sept. 12 |
| 3. Existence and extension | 3.11 | Sept. 12 | 4. Denumerable Probabilities | 4.1, 4.3, 4.4, 4.7, 4.11(a,e) | Sept. 19 | 5. Simple Random Variables | 5.1, 5.17(a) | Sept. 19 | 5. Simple Random Variables | 5.5(a), 5.12, 5.17(b) | Sept. 26 | 6. The law of large numbers | 6.11, 6.13 | Sept. 26 | 10. General measures | 10.2, 10.3, 10.4 | Oct. 3 | 11. Uniqueness and Extension | 11.2(b) | Oct. 3 | 12 Measures in Euclidean space | 12.1 | Oct. 17 | 13 Measurable Functions and Mappings | 13.1, 13.8, 13.17 | Oct. 17 | 14 Distribution functions | 14.3(a), 14.5, 14.8 | Oct. 24 | 15 The integral | 15.2 | Oct. 31 | 16 Properties of the integral | 16.1(a), 16.3, 16.4(a) | Oct. 31 | 16 Properties of the integral | 16.8, 16.9 | Nov. 7 | 18 Product measure and Fubini Theorem | 18.1, 18.6, 18.14 | Nov. 14 | 20 Random variables and distribution functions | 20.5, 20.6, 20.8 | Nov. 21 | 20 Random variables and distribution functions | 20.9, 20.12, 20.13, 20.15, 20.20 | Nov. 30 | 21 Expected values | 21.9, 21.21 | Dec. 5 | 22 Sums of independent random varaibles | 22.15, S1, S2. | Feb. 1 | 9 Large Deviations and The law of iterated logarithm | 9.4, 9.5, S3, S4, S5. | Feb. 8 | 23 Poisson process | 23.1, 23.3, 23.5, 23.6, 23.12 | Feb. 15 | 25 Weak Convergence | 25.4, 25.6, 25.7, 25.17 | Feb. 22 | 26 Charactersitic functions | 26.1, 26.2, 26.6, 26.10, 26.12 | Mar. 1 | 27 Central Limit Theorem | 27.3, 27.4, 27.6 27.10, 27.14 | Mar. 828 Infinitely Divisible distributions | 28.1, 28.3 | Mar. 29 | 29 Limit Theorems in higher dimensions | 29.2 (a)-(c), 29.3(b) 29.6 | Mar. 29 | 30 Method of moments | 30.3, 30.4. 30.5 (a), 30.7 | Apr. 7 | 32 Radon-Nikodym Theorem | 32.5, 32.6, 32.9, 32. 10 | Apr. 12 | 33 Conditional Probability | 33.7, 33.13, S6, S7 | Apr. 19 | 34 Conditional Expectation | 34.2 34.10, S6, S7 | May 3 | 35 Martingales | 35.2, 35.6, 35.7 | May 3 |