In the course we treat the following topics.
Sample spaces, probability measures, distribution functions, random variables with discrete and continuous distributions, functions of random variables, multivariate distributions, random vectors, independent random variables, conditional distributions, functions of random vectors and their distributions, expectation and variance, covariance and correlation, the law of large numbers, central limit theorem, chi-square and t-distributions, estimation, method of moments, maximum likelihood, large sample theory, confidence intervals, Cramer-Rao bound, hypothesis testing, Neyman-Pearson paradigm, likelihood ratio tests, confidence intervals, linear regression, least squares estimation of regression parameters, testing regression hypotheses.
2nd EDITION | 3rd EDITION |
pages 202-203 | pages 216-218 |
section 8.6 | section 8.7 |
sections 9.1-9.3 | sections 9.1-9.2 |
section 9.4 | section 9.3 |
section 9.5 | section 9.4 |
FROM WEEK TO WEEK | |
1 | Rice, chapter 2 and 3 (main themes only); students should study the many examples of distributions themselves, but skip parts of chapter 3
that require more than basic knowledge of multiple integrals.
Exercises: chapter 2: 5, 23, 33, 41, 44*, 53, 55*, 59*; chapter 3: 7, 17(a,b), 32(a), 34*, 37*, 38 |
2 | Rice, sections 4.1-4.3 (except Markov and Chebychev inequalities)
Exercises: chapter 4: 2, 4, 6, 12, 31, 34*, 45*, 46*, 53*, 71(a) Homework: chapter 4: 32, 45 (due November 10) |
3 | Rice, chapter 5 (skip the considerations involving moment generating functions),
sections 6.1, 6.2, 6.3, extra on multivariate normal distributions (see slides)
Exercises: chapter 5: 1*, 3*, 9, 12*, 13, 15, 17*, 23, 26 Homework: chapter 5: 16, chapter 6: 9 (due November 17) |
4 | Rice, sections 8.3-8.5.2 (Theorem B next week)
Exercises: chapter 8: 4*, 5*, 8, 17* and (in the numbering of the 3rd!! edition) 5abc, 12 (ignore all questions on Fisher information and on sufficient statistics) Homework: chapter 8: 14abc, 19ab (due November 24) |
5 | Rice, sections 8.5.2 (continued) 8.5.3 (you also read pages 202, 203 in the 2nd edition, pages 217, 218 in the 3rd edition), 8.6, and a small part of 9.2
Exercises: chapter 8: 39abc*, 42, 44abc, 49, 52* Homework: chapter 8: 17, 33 chapter 9: 2 (due December 1) and read section 9.2 until the Neyman-Pearson lemma |
6 | Rice, sections 9.2, 9.3, 9.5 (very briefly)
Exercises: chapter 9: 1, 3*, 5, 7*, 9, read section 9.4 and pay special attention to the second half of page 302 (on p-value) as well Homework: chapter 9: 11, 16 (due December 8) |
7 | Rice, sections 9.4, 14.1-14.4 (emphasis on 14.3, 14.4)
Exercises: chapter 9: 15*, chapter 14: 3*, 4, 8*, 9, 12*, 15 Homework: chapter 14: 5, 16, 25* (due December 15) |