| Lecture | Section | Topics |
|---|---|---|
| 1 | (1.4, 7.2) | Quick review of basics, including inclusion-exclusion formula and expectation of sum of random variables |
| 2 | 7.3 | Variance of sum of random variables |
| 3 | 1.5, (2.5) | Multinomial coefficient, example 5h on p. 42 (*) |
| 4 | 1.6, (2.5) | Balls in urns, runs of success (example 51, p. 47) (*) |
| 5 | (2.5) | Matching (example 5j on p. 44) (*) |
| 6 | 4.9.3, (7.2-3) | Hypergeometric distribution (includes example 2g of Sec. 7.2 and example 3d of 7.3) (*) |
| 7 | 4.9.2 | Negative binomial distribution (includes example 2f of Sec. 7.2) (*); Banach match problem |
| 8-9 | (6.1), (7.3) | Multinomial distribution; correlation coefficient |
| 10-11 | 7.2, 7.3 | More examples of uses of indicators |
| 12-14 | 3.5 | Multiple conditioning |
| 15-17 | 6.4, 6.5, 7.4 | Conditional distribution, expectation and variance |
| 18-19 | 7.6 | Moment generating function |
| 20 | 7.7, (7.6) | Multivariate normal and joint moment generating function |
| 21-22 | 6.6 | Order statistics |
| 23 | 8.2 | Chebyshev's inequality and the weak law of large numbers |
| 24-25 | 8.3 | Central limit theorem |
(*) It is proposed that computations of expectations and variances using indicators be done in connection to new problems and models being introduced.
( ) Sections indicated withing parenthesis are relevant to the lecture but only as far as a small part of it is concerned.