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 1 |
Rice, chapter 1
Exercises: chapter 1: 1, 4, 5, 11, 19, 27, 33, 53, 57, 63, 65 |
| Lecture 2 | Rice, chapter 2
Exercises: chapter 2: 3, 5, 13, 21, 23, 27, 33, 41, 44, 53, 55, 59 |
| Lecture 3 | Rice, (parts of) sections 3.1, 3.2, 3.3, 3.4, 3.6
Exercises: chapter 3: 1, 3, 7, 17(a,b), 32, 34, 37, 38, 55, 57 |
| Lecture 4 | Rice, (parts of) sections 3.5, 4.1, 4.2, 4.3, 4.4
Exercises: chapter 4: 2, 4, 6, 12, 31, 34, 45, 46, 53, 64, 65, 71 |
| Lecture 5 | Rice, chapter 5 (skip the considerations involving moment generating functions),
sections 6.1, 6.2, extra on multivariate normal distributions (see transparancies) Exercices: chapter 5: 1, 3, 9, 12, 13, 15, 17, 23, 26 |
| Lecture 6 | Rice, sections 8.3-8.5.2, part of 8.5.3, 8.6
Exercises: chapter 8: 4, 5, 8, 17, 19ab, 39, 42, 44, 49, Cauchy-Schwartz inequality |
| Lecture 7 | Rice, sections 8.5.3,
9.1-9.5
Exercises: chapter 8: 52, chapter 9: 1, 2, 3, 5, 7, 9, 12, 15, 18, 7, 21 |
| Lecture 8 | Rice, sections 14.1-14.4
Exercises: chapter 9: 1, 3, 4, 8, 9, 11, 20, 24, 25, 31 |