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, Chapters 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. There may be some additional exercises by the TA (also in subsequent weeks)! Homework: none. |
2 | Rice, Sections 4.1-4.3 (except Markov inequality, but you can read it yourself).
Exercises: Chapter 4: 2, 4, 6, 12, 31, 34*, 46*, 53*, 71(a). Homework: Chapter 4: 32, 45 (due Friday September 13, 12:00 (noon)) and read the two slides on dependence and correlation. Examples of exam questions: 1, 5, 11, 13, 19(a-d). |
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 September 20). Examples of exam questions: 37(a,e), 40(a,h,i). |
4 | Rice, sections 8.3-8.5.2
Exercises: chapter 8: 5*(ab), 8, 17*(ab) 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 September 27). Examples of exam questions: 10, 15, 16 (ignore parts on theory that has not been treated yet). |
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: 33 (numbering of the 3rd edition); chapter 9: 2 (due October 4) and read section 9.2 until the Neyman-Pearson lemma. Examples of exam questions: 10d, 15d,e, 16e,f. |
6 | Rice, sections 9.2, 9.3, 9.5 (very briefly), perhaps also 9.4.
Exercises: chapter 9: 1, 3*, 5, 7*, 9; read the section on the generalized likelihood ratio test. Homework: chapter 9: 11, 16 (due October 11). Examples of exam questions: 20, 27. |
7 | Confidence intervals and testing, regression; Rice, sections 9.4, 14.1-14.4 (emphasis on 14.3, 14.4).
Exercises (might be changed): chapter 9: 15*, chapter 14: 3*, 4, 8*, 9, 12*, 15. Homework (optional!): chapter 14: 5, 16, 25* (due October 18). Examples of exam questions: 8, 18, 24, 39. |