Math 3081 (Probability and Statistics), Summer-II 2020
| Course Information | |||||
|---|---|---|---|---|---|
| Instructor | Class Times | Office Hours | |||
| Evan Dummit edummit at northeastern dot edu |
(Section 1) MTWR, 1:30pm-3pm (Section 2) MTWR, 10am-11:30am Online, via Zoom |
3:10pm-4:10pm M or by appointment Online, via Zoom |
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| There are two sections of Math 3081, corresponding to the two lecture times listed. You are requested to attend your assigned lecture, but in the event you are not able, you are allowed to attend the other one (the lectures will cover the same content at the same pace). All lectures will be recorded and made available for on-demand viewing at any time. | |||||
| Math 3081 uses a Piazza page for course discussion. Links to all of the live lectures, office hours, problem sessions, and lecture recordings are hosted there. | |||||
| Teaching Assistants | Recitation Times | Office Hours | |||
| Aleksei Pakharev (pakharev.a at northeastern dot edu) Cancan Zhang (zhang.can at husky dot neu dot edu) |
(Session 1) 3pm-4pm W (Cancan Zhang) (Session 2) 4pm-5pm W (Aleksei Pakharev) (Session 3) 3pm-4pm R (Cancan Zhang) (Session 4) 4pm-5pm (Aleksei Pakharev) Online, via Zoom |
noon-1pm W (CZ) noon-1pm R (AP) Online, via Zoom |
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| For detailed information about the course, please consult the 3081 Course Syllabus. (Note: any information given in class or on this webpage supersedes the written syllabus.) | |||||
| All homework assignments are available on the 3081 WeBWorK page. | |||||
| Handouts / Lecture Notes | |||||
|---|---|---|---|---|---|
| The instructor will write lecture notes for the course in place of an official textbook as the semester progresses. The course will follow the presentation in Larsen and Marx's "An Introduction to Mathematical Statistics and its Applications" (5th edition), but it is not necessary to purchase the textbook for this course. For those students who are using the textbook, here are the correspondences between the notes and textbook: Notes ch1: Book §2.1-2.7 (Probability) Notes ch2: Book §3.1-3.9 + §4.1-4.3 (Random Variables) Notes ch3: Book §5.1-5.4 (Parameter Estimation) Notes ch4: Book §6.1-6.4 + §7.1-7.5 + §9.1-9.5 + §10.1-10.4 (Hypothesis Testing) |
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| Handout | Topics | ||||
| Chapter 1: Counting and Probability (26pp, v2.00, posted 6/27) | 1.1 ~ Sets and Set Operations 1.2 ~ Counting Principles 1.3 ~ Probability and Probability Distributions 1.4 ~ Conditional Probability and Independence |
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| Chapter 2: Random Variables (34pp, v2.20, updated 7/19) (updates in v2.20: typo fixes) (updates in v2.15: added missing property of covariance) (updates in v2.10: fixed typos, added Chebyshev's inequality to 2.2.2) |
2.1 ~ Discrete Random Variables 2.2 ~ Continuous Random Variables 2.3 ~ The Normal Distribution, Central Limit Theorem, and Modeling Applications |
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| Chapter 3: Parameter and Interval Estimation (18pp, v1.25, updated 8/2) (updates in 1.25: standardized use of confidence interval notation with §4) (updates in 1.10: more typo fixes) (updates in 1.05: typo fixes) |
3.1 ~ Parameter Estimation 3.2 ~ Interval Estimation |
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| Chapter 4: Hypothesis Testing (50pp, v1.01, updated 8/11) (updates in v1.01: typo fix) (updates in v1.00: added 4.3.2-4.3.3) (updates in v0.85: added 4.2.5-4.3.1, added matched pairs to 4.2.4, fixed typos) (updates in v0.75: added 4.2.3-4.2.4, fixed typos) (updates in v0.50: added 4.1.4-4.2.2, fixed typos) |
4.1 ~ Principles of Hypothesis Testing 4.2 ~ The t Distribution and t Tests 4.3 ~ The χ2 Distribution and χ2 Tests |
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| Lecture Slides | |||
|---|---|---|---|
| These are the slides used during the lectures. They will usually be posted ahead of the lecture time. | |||
| Date | Material | ||
| Mon, Jun 29th Tue, Jun 30th Wed, Jul 1st Thu, Jul 2nd |
Lecture 1: Welcome + Sets and Counting (Notes 1.1)
Lecture 2: Counting Principles (Notes 1.2) [Typos fixed] Lecture 3: Sample Spaces and Probability (Notes 1.3.1-1.3.3) [Typos fixed] Lecture 4: Conditional Probability (Notes 1.3.3+1.4.1) [More typos fixed] |
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| Mon, Jul 6th Tue, Jul 7th Wed, Jul 8th Thu, Jul 9th |
Lecture 5: Independence (Notes 1.4.2) [Typos fixed]
Lecture 6: Bayes' Formula and Applications of Probability (Notes 1.4.3) [Typos fixed] Lecture 7: Discrete Random Variables, Part 1 (Notes 2.1.1-2.1.3) [Typos fixed] Lecture 8: Discrete Random Variables, Part 2 (Notes 2.1.3-2.1.5) |
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| Mon, Jul 13th Tue, Jul 14th Wed, Jul 15th Thu, Jul 16th |
Lecture 9: Continuous Random Variables, Part 1 (Notes 2.1.6-2.2.1) [Typos fixed]
Lecture 10: Continuous Random Variables, Part 2 (Notes 2.2.2-2.2.3) [Updated] Lecture 11: Continuous Random Variables, Part 3 (Notes 2.2.3-2.2.4) [Typos fixed] Lecture 12: The Normal Distribution and Central Limit Theorem (Notes 2.3.1-2.3.2) |
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| Mon, Jul 20th Tue, Jul 21st Wed, Jul 22nd Thu, Jul 23rd |
Lecture 13: Applications of the Central Limit Theorem (Notes 2.3.2) [Typos fixed]
Lecture 14: Poisson and Exponential Distributions (Notes 2.3.3-2.3.4) [Typos fixed] Lecture 15: Maximum Likelihood Estimates (Notes 3.1.1-3.1.2) [Typos fixed] Lecture 16: Properties of Estimators: Bias and Efficiency (Notes 3.1.2-3.1.3) |
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| Mon, Jul 27th Tue, Jul 28th Wed, Jul 29th Thu, Jul 30th |
Lecture 17: Confidence Intervals, Part 1 (Notes 3.2.1) [Updated]
Lecture 18: Confidence Intervals, Part 2 (Notes 3.2.2) [Typos fixed] Lecture 19: Hypothesis Testing and z Tests (Notes 4.1.1-4.1.2) [Updated] Lecture 20: More z Tests (Notes 4.1.2-4.1.3) [Typos fixed] |
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| Mon, Aug 3rd Tue, Aug 4th Wed, Aug 5th Thu, Aug 6th |
Lecture 21: Unknown Proportion + Testing Errors (Notes 4.1.3-4.1.4) [Typos fixed]
Lecture 22: Testing Errors + t Distributions (Notes 4.1.4-4.2.1) [Updated] Lecture 23: t Distributions and Confidence Intervals (Notes 4.2.1-4.2.2) Lecture 24: One-Sample t Tests (Notes 4.2.3) [Typos fixed] |
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| Mon, Aug 10th Tue, Aug 11th Wed, Aug 12th |
Lecture 25: Two-Sample t Tests (Notes 4.2.4)
Lecture 26: Robustness and the χ2 Distribution (Notes 4.2.5-4.3.2) Lecture 27: The χ2 Tests for Goodness-of-Fit and Independence (Notes 4.3.2-4.3.3) |
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| Exam Information | |||
|---|---|---|---|
| Exams will be distributed and collected via the 3081 Blackboard page. A list of exam testing windows will be posted on Piazza for you to choose among (ahead of the exam). You will then download, take, and then upload scans of your exam responses during your testing window. | |||
| Exam | Date, Time, Location | Topics | Review Material |
| Exam 1 (Form A), (sols) (Form B), (sols) (Form C), (sols) |
Sat, Jul 11th Via Blackboard |
Lectures 1-7 WeBWorKs 1-2 Notes §1.1-1.4 + §2.1.1-2.1.3 |
Review problems,
(answers) Review session on Fri Jul 10th |
| Exam 2 (Form A), (sols) (Form B), (sols) (Form C), (sols) (Form D), (sols) |
Sat, Jul 25th Via Blackboard |
Lectures 8-14 WeBWorKs 3-4 Notes §2.1-2.3 |
Review problems,
(answers) Review session on Fri Jul 24th |
| Exam 3 (Form A), (sols) (Form B), (sols) |
Sat, Aug 8th Via Blackboard |
Lectures 15-23 WeBWorKs 5-6 Notes §3.1-3.2 + §4.1-4.2.2 |
Review problems,
(answers) Review session on Fri Aug 7th |
| Final | Mon, Aug 17th or Tue, Aug 18th Via Blackboard |
WeBWorKs 1-7 Notes §1.1-4.3 |
Supplementary review problems, (answers) Review sessions TBA |
| Bring your University ID to all exams. Calculators may be used, provided they do not have qwerty keyboards and cannot do symbolic algebra. You are permitted one "cheat sheet", consisting of a single-sided 8.5in-by-11in piece of paper. Cell phones, other electronic devices, books, and additional notes of any kind will NOT be permitted in exams. | |||
| Old Exams | |||
|---|---|---|---|
| These are exams from previous Math 3081 courses, and are provided to give you an additional source of practice problems. Please note: some courses may have been organized differently than this course, so some material may differ from exam to exam. Some topics from our course may be covered or emphasized differently, or skipped altogether, and some topics on these exams may not appear on the exams in this course. | |||
| Exam 1 | Exam 2 | Exam 3 | Final Exam |
|
2018 Summer 1 (with solutions) 2019 Summer 2, (solutions) |
2018 Summer 1, (solutions) 2019 Summer 2, (solutions) |
2018 Summer 1, (solutions) 2019 Summer 2, (solutions) |
2017 Spring, (solutions) 2017 Spring, (solutions) 2017 Spring, (solutions) 2017 Summer 2 (with solutions) 2018 Spring, (solutions) 2018 Summer 1, (solutions) |
| Tips For Success In This Course | |||
|---|---|---|---|
| Attend Lecture | Missing lecture is a bad idea! If for any reason you cannot make it to a class, you should watch the recording of the lecture. You are responsible for all material covered in lecture. | ||
| Read the Lecture Notes (or Textbook) | The lecture notes and the textbook are comprehensive sources of material for the course. The notes are intended as review material, although many students like to read them as preparation before attending the lecture on the corresponding topics. Please note that the electronic notes are not identical to the material covered in class: this is by design, so as to provide you a slightly different perspective on the material. | ||
| Use WeBWorK Effectively | WeBWorK assignments are intended to help you learn the course material at a basic level. Look over the problems well before the due date, and work on them in concert with the corresponding lectures. You may use technology (calculators, Wolfram Alpha, computer software) and other people to help you (so long as you are submitting your own work), but be mindful: if you do not understand how to do the WeBWorK problems, you will almost certainly struggle on the exams! (Exam problems are often harder than WeBWorK problems.) | ||
| Attend Office Hours | Office hours are specifically reserved for you to receive individual, one-on-one help from the instructor or TAs. Office hours will be the most effective when you have already put in effort to learn the material on your own (including trying to solve the homework problems), and when you come in with a list of specific questions or topics you are struggling with. | ||
| Use Tutoring Services | The university offers a wide variety of free tutoring services. Over the summer, the Tutoring Center is open for students taking various math courses, including Math 3081. | ||
| Course Schedule | |||
|---|---|---|---|
| The schedule is subject to change! All sections refer to the course lecture notes. | |||
| Week | Schedule | ||
| Week of June 29 (class starts 6/29) |
§1.1: Sets and Set Operations §1.2: Counting Principles §1.3: Probability and Probability Distributions §1.4.1: Conditional Probability WeBWorK 1 due Sunday 7/5 at 5am Eastern. |
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| Week of July 6 | §1.4.2: Independence §1.4.3: Computing Probabilities, Bayes' Formula §2.1.1: Discrete Random Variables §2.1.2: Expected Value §2.1.3: Variance and Standard Deviation §2.1.4: Joint Distributions WeBWorK 2 due Friday 7/10 at 5am Eastern. Review for Exam 1 EXAM 1 online Saturday, July 11th |
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| Week of July 13 | §2.1.5: Independence §2.1.6: Covariance and Correlation §2.2: Continuous Random Variables WeBWorK 3 due Friday 7/17 at 5am Eastern. |
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| Week of July 20 |
§2.3: The Normal Distribution, Central Limit Theorem, and Modeling Applications §3.1.1: Maximum Likelihood Estimates §3.1.2: Biased and Unbiased Estimators §3.1.3: Efficiency of Estimators WeBWorK 4 due Friday 7/24 at 5am Eastern. Review for Exam 2 EXAM 2 online Saturday, July 25th |
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| Week of July 27 | §3.2: Interval Estimation §4.1.1: Hypothesis Testing §4.1.2: One-Sample and Two-Sample z Tests §4.1.3: z Tests for Unknown Proportion WeBWorK 5 due Friday 7/31 at 5am Eastern. |
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| Week of August 3 | §4.1.3: z Tests for Unknown Proportion §4.1.4: Errors in Hypothesis Testing §4.2.1: The t Distribution §4.2.2: Confidence Intervals Using t Statistics §4.2.3: One-Sample t Tests WeBWorK 6 due Friday 8/7 at 5am Eastern. Review for Exam 3 EXAM 3 online Saturday, August 8th |
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| Week of August 10 (class ends 8/12) |
§4.2.4: Two-Sample t Tests §4.2.5: Robustness of t Tests §4.3.1: The χ2 Distribution §4.3.2: The χ2 Test for Independence §4.3.3: The χ2 Test for Goodness of Fit WeBWorK 7 due Friday 8/14 at 5am Eastern. Review for Final Exam |
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| Week of August 17 |
FINAL EXAM online Monday, August 17th or Tuesday, August 18th | ||