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 | 9/18 | Definitions of probability | Chap. 1 | 1.2, 1.4, 1.6, 1.8, 1.9 | |
| 2 | 9/25 | Inclusion–exclusion principle, independence, conditional probability | Secs. 2.1–2.3 | 2.2, 2.5, 2.6, 2.7, 2.10 | |
| 9/28 | Total proabability and Bayes’ formulas, random variables, discrete distributions | Secs. 2.4–3.2 | 2.12, 2.14, 2.17, 2.20, 3.4, 3.5 | Homework 1 complete, due 10/9 |
| 3 | 10/2 | National Day | | | |
| 4 | 10/9 | Continuous distributions, transformations of random variables | Secs. 3.3, 3.4 | 3.7, 3.9, 3.12, 3.14, 3.20 | |
| 10/12 | Random vectors, independence | Secs. 4.1–4.4.A | 4.3, 4.5, 4.6, 4.7 | |
| 5 | 10/16 | Transformations of random vectors, bivariate normal distributions, conditional distributions | Secs. 4.4.B–4.7 | 4.12, 4.13, 4.15, 4.19 | Homework 2 complete, due 10/23 |
| 6 | 10/23 | Expectation | Secs. 5.1–5.4 | 5.4, 5.6, 5.8, 5.11 | |
| 10/26 | Variance and covariance | Secs. 5.5–5.7 | 5.17, 5.20, 5.21, 5.24 | |
| 7 | 10/30 | Midterm 1
Strong law of large numbers | Sec. 6.1 | | Midterm 1: mean = 42, median = 42, Q1 = 30, Q3 = 55, high score = 95 |
| 8 | 11/6 | Weak law of large numbers, central limit theorem | Secs. 6.2, 6.3 | 6.3, 6.7, 6.8, 6.10 | Homework 3 complete, due 11/9 |
| 11/9 | Descriptive statistics, survey sampling | Secs. 7.1–7.3 | | |
| 9 | 11/13 | Box plots, randomized experiments, parameter estimation, method of moments | Secs. 7.4–8.2 | 8.1, 8.3, 8.4, 8.5 | |
| 10 | 11/20 | Maximum likelihood estimation, interval estimation for one normal population | Secs. 8.3–9.1.C | 8.8, 8.12, 8.13, 8.14, 9.2 | |
| 11/23 | Interval estimation for two normal populations and for nonnormal populations | Secs. 9.1.D–9.4 | 9.9, 9.12, 9.15, 9.19 | Homework 4 complete, due 11/27 |
| 11 | 11/27 | Hypothesis testing, tests for normal means | Secs. 10.1–10.3 | 10.6, 10.7, 10.12, 10.13 | |
| 12 | 12/4 | Tests for variances, Q-Q plots and goodness-of-fit tests | Secs. 10.4, 11.1 | 10.11, 10.15, 11.1 | |
| 12/7 | Midterm 2
Tests for proportions | Sec. 11.2 | 11.3, 11.7 | Midterm 2: mean = 52, median = 51, Q1 = 42, Q3 = 65, high score = 100 |
| 13 | 12/11 | Tests of independence for contingency tables, p-values and power functions | Secs. 11.3, 11.4 | 11.9, 11.11, 11.12, 11.13 | Homework 5 complete, due 12/18 |
| 14 | 12/18 | Tests for correlation coefficients, simple linear regression | Secs. 12.1–12.3.A | 12.1 | |
| 12/21 | Simple linear regression | Secs. 12.3.B–E | 12.2, 12.3 | |
| 15 | 12/25 | Analysis of variance | Chap. 13 | 13.1, 13.2 | Homework 6 complete, due 1/4 |
| 16 | 1/1 | New Year's Day | | | |
| 1/4 | Sampling from the normal distribution | Casella & Berger Sec. 5.3 | | |
| 17 | 1/8 | Final exam | | | Mean = 53, median = 54, Q1 = 38, Q3 = 72, high score = 93
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