00132380: Probability Theory and Statistics (B)
Course Description
This is an undergraduate upper-level course for students majoring in science, engineering, and other fields where applied probability and
statistics play an essential role. Topics covered include basic concepts of probability, random variables and vectors, expectation and variance,
laws of large numbers and central limit theorems, descriptive statistics, point and interval estimation, hypothesis testing, simple linear
regression, analysis of variance, and additional topics when time permits.
Syllabus
Lectures and Assignments
| Week | Date | Topics | References | Assignments | Notes |
| 1 | 2/20 | Classical probability | Secs. 1.1, 1.2 | | |
| 2 | 2/25 | Axioms and rules of probability | Secs. 1.3–2.3 | 1.2, 1.4, 1.6, 1.8, 1.9, 2.2, 2.5, 2.6, 2.7, 2.10 | |
| 2/27 | Law of total proabability, Bayes’ theorem, discrete random variables | Secs. 2.4–3.2 | 2.12, 2.14, 2.17, 2.20, 3.4, 3.5 | Homework 1 complete, due 3/6 |
| 3 | 3/6 | Continuous random variables | Sec. 3.3 | 3.7, 3.8, 3.9 | |
| 4 | 3/11 | Transformations of random variables, discrete random vectors | Secs. 3.4–4.2 | 3.12, 3.14, 3.20, 4.3, 4.5 | |
| 3/13 | Continuous random vectors, transformations, bivariate normal distributions | Secs. 4.3–4.6 | 4.6, 4.7, 4.10, 4.12, 4.14, 4.16 | Homework 2 complete, due 3/20 |
| 5 | 3/20 | Conditional distributions, expectation | Secs. 4.7–5.3 | 4.19, 5.2, 5.3, 5.6, 5.8 | |
| 6 | 3/25 | Expectation, variance | Secs. 5.4, 5.5 | 5.10, 5.11, 5.22, 5.24 | |
| 3/27 | Covariance | Secs. 5.6, 5.7 | 5.17, 5.20 | Homework 3 complete, due 4/3 |
| 7 | 4/3 | Laws of large numbers, central limit theorem | Chap. 6 | 6.3, 6.7, 6.8, 6.10 | |
| 8 | 4/8 | Descriptive statistics, survey sampling | Chap. 7 | | |
| 4/10 | Midterm review | | | |
| 9 | 4/17 | Midterm exam | | | Mean = 58, median = 61, Q1 = 45, Q3 = 76, high score = 91 |
| 10 | 4/22 | Properties of point estimators, sample mean and variance | Sec. 8.1 | 8.1, 8.3, 8.4 | |
| 4/24 | Method of moments, maximum likelihood estimation | Secs. 8.2, 8.3 | 8.5, 8.8, 8.12, 8.13, 8.14 | Homework 4 complete, due 5/6 |
| 11 | 5/1 | No class | | | |
| 12 | 5/6 | Confidence intervals for normal populations | Secs. 9.1, 9.2 | 9.2, 9.9, 9.12 | |
| 5/8 | Confidence intervals for nonnormal populations, sampling distributions | Secs. 9.3, Larsen & Marx Sec. 7.3 | 9.15, 9.19, Larsen & Marx 7.3.11, 7.3.13 | |
| 13 | 5/15 | Hypothesis testing, tests for normal means | Secs. 10.1–10.3 | 10.3, 10.6, 10.7, 10.12, 10.13 | Homework 5 complete, due 5/20 |
| 14 | 5/20 | Tests for variances, proportions, and distribution functions | Secs. 10.4–11.2 | 10.15, 11.1, 11.3, 11.7 | |
| 5/22 | Contingency tables, p-values, least squares | Secs. 11.3–12.2 | 11.9, 11.11, 12.1 | |
| 15 | 5/29 | Simple linear regression | Sec. 12.3 | 12.2, 12.3 | |
| 16 | 6/3 | Analysis of variance | Chap. 13 | 13.1, 13.2 | Homework 6 complete, due 6/5 |
| 6/5 | Final review | | | |
| 17 | 6/10 | Final exam | | | Mean = 44, median = 45, Q1 = 37, Q3 = 59, high score = 70
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