Link(s):
Weekly postings:
| Posted on/by | Reading | Homework problems | Due date | Basic problems |
| 9/18 | Sections 1.1-1.4 in the text. Handout "Events and probabilities" | Some of Problems 1-7 (6 points; extra points will not be counted) | 10/8 | Problems 1, 2, 4, 6 |
| 9/23 | Sections 1.5-1.6 in the text. Handout "Random variables" (till Example 7) | Some of Problems 8-13 (12 points; extra points will not be counted) | 10/15 | Problems 9, 10(a), 11, 12, 13(a)(b) |
| 10/2 | Section 1.7 in the text. Handouts "Random variables" and "Quantile and expectation" (till Example 5) | Some of Problems 14-21 (8 points; extra points will not be counted) | 10/22 | Problems 14-18 |
| 10/9 | Sections 1.8 - 1.9 in the text. Handouts "Quantile and expectation" and "Some special expectations" (till Example 3; Var(X) in Example 3 has not been computed) Additional handout "range of a transformed variable" with an explanation file (mp4) | Some of Problems 22-28 (8 points; extra points will not be counted) | 10/29 | Problems 22-25, 28 |
| 10/16 | Sections 1.9 and 2.1 (before 2.1.2) in the text. Handouts "Some special expectations" and "Joint distribution of a vector of random variables" | Some of Problems 29-34 (10 points; extra points will not be counted) | 11/5 | Problems 29-33 |
| 10/23 | Sections 2.1.2 and 2.2 in the text. Handouts "Expectation of g(X,Y)" and "Distribution of a transformed random vector". Details of evaluating a bivariate integral using change of variable can be found in "Integration for bivariate functions" | Some of Problems 35-39 (10 points; extra points will not be counted) | 11/19 | Problems 35-38 |
| 10/30 | Sections 2.3 and 2.4 in the text. Handouts "Conditional distributions and expectations" and "Independent random variables". | Some of Problems 40-43 (12 points; extra points will not be counted) | 11/26 | Problems 40-42 |
| 11/6 | Sections 2.6-2.7 (skip Section 2.6.1). The definition of a normal distribution can be found in Section 3.4. Handouts "Independent random variables" (Example 4 and the definition of a normal distribution), "Independence of two random vectors" and "Distribution of a transformed random vector" (till Example 1). | Some of Problems 44-48 (10 points; extra points will not be counted) | 12/3 | Problems 44,45,48 |
| 11/20 | Section 2.5 in the text. Handouts "Distribution of a transformed random vector" and "Covariance and correlation" (till Example 4 Part (a)) | Some of Problems 49-54 (10 points; extra points will not be counted) | 12/10 | Problems 49(a), 50-51, 54 |
| 11/27 | Handouts "Covariance and correlation" and "Multivariate normal distributions" (till Example 4) The definition of a multivariate normal distribution can be found in Section 3.5 in the text. | Some of Problems 55-59 (9 points; extra points will not be counted) | 12/20 (was due 12/17) | Problems 56,58 |
| 12/4 | Handout "Multivariate normal distributions" (till Example 6(a)) The definition of a multivariate normal distribution can be found in Section 3.5 in the text. The definition of a covariance matrix can be found in Section 2.6.1. | Some of Problems 60-62 (8 points; extra points will not be counted) | 12/24 | Problem 62 |
| 12/11 | Handouts "Multivariate normal distributions" and "Some special distributions" (till Example 1) The definition of a multivariate normal distribution can be found in Section 3.5 in the text. The definition of a covariance matrix can be found in Section 2.6.1. The definition of a binomial distribution can be found in Section 3.1. | Some of Problems 63-66 (8 points; extra points will not be counted) | 12/24 | Problems 63,66 |
| 12/18 | Handouts "Finding a joint PDF using conditional and marginal PDFs" and "Some special distributions" (till Fact 3). Definitions of some distributions can be found in Sections 3.1-3.3 in the text. | Some of Problems 67-68 (4 points; extra points will not be counted) | 12/24 | Problems 67-68 |
| Handout "Probability calculation based on MGF" |