In the course we treat the following topics.
Sample spaces, probability measures, conditional probability, independent events, 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, conditional expectation, the law of large numbers, central limit theorem, chi-square and 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.
| Lecture 1a | Rice, chapter 1
Exercises: chapter 1: 1, 4, 5, 11, 19, 27, 33, 53, 57, 63, 65 |
| Lecture 1b | Rice, chapter 2
Exercises: chapter 2: 3, 5, 13, 21, 23, 27, 33, 41, 44, 53, 55, 59 |
| Lecture 2a | Rice, sections 3.1-3.4, 3.6 (not all details, skip parts
that require more than basic knowledge about multiple integrals)
Exercises: chapter 3: 1, 3, 7, 17(a,b), 32, 34, 37, 38, 55, 57 |
| Lecture 2b | Rice, sections 3.5, 4.1-4.4 (also read about correlation, which has not been
treated in the classes)
Exercices: chapter 4: 2, 4, 6, 12, 31, 34, 45, 46, 53, 64, 65, 71 |
| Lecture 3a | Rice, chapter 5 (skip the considerations involving moment generating functions),
sections 6.1, 6.2, extra on multivariate normal distributions
Exercices: chapter 5: 1, 3, 9, 12, 13, 15, 17, 23, 26 |
| Lecture 3b | Rice, sections 8.3-8.5.2, 8.6
Exercises: chapter 8: 4, 5, 8, 17, 19ab, 39, 42, 44, 49 |
| Lecture 4a | Rice, section 6.3, sections 8.5.3 (you also read pages 202, 203), 9.1-9.4
Exercises: chapter 8: 52, chapter 9: 1, 2, 3, 5, 7, 9, 12, 15, 18, 7, 21 |
| Lecture 4b | Rice, section 9.5, sections 14.1-14.4
Exercises: 1, 3, 4, 8, 9, 11, 20, 24, 25, 31 |