Math 3081 (Probability and Statistics), Summer-II 2022
| Course Information | |||||
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| Instructor | Class Times | Office Hours | |||
| Evan Dummit edummit at northeastern dot edu |
(Sec 1) MTWR, 1:30pm-3:10pm, Hurtig 130 (Sec 2) MTWR, 9:50am-11:30am, Dodge 050 |
R 3:30pm-5:30pm or by appointment Online, via Zoom |
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| There are two sections of Math 3081, corresponding to the two lecture times listed. The lectures will cover the same material at the same pace. | |||||
| 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.) | |||||
| Teaching Assistant | Problem Session / Office Hours | ||||
| Jiewei Feng feng.ji at northeastern dot edu |
F, 1pm-3pm Online, via Zoom |
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| Nathan Zelesko zelesko.n at northeastern dot edu |
F, 3pm-5pm Online, via Zoom |
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| 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. | |||||
| All homework assignments are available on the 3081 WeBWorK page. All problems have unlimited attempts and you may work on the assignments at any time up until the due date. Your username is your Northeastern username, and your password is your 7-digit Northeastern ID number without the two leading zeroes. | |||||
| 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 (Hypothesis Testing) Notes ch5: Book §9.1-9.5 + §10.1-10.4 (Topics in Hypothesis Testing) |
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| Handout | Topics | ||||
| Chapter 1: Counting and Probability (25pp, v3.00, posted 6/21) | 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, v3.00, posted 7/7) | 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, v3.00, posted 7/25) | 3.1 ~ Parameter Estimation 3.2 ~ Interval Estimation |
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| Chapter 4: Hypothesis Testing (21pp, v3.00, posted 8/2) | 4.1 ~ Principles of Hypothesis Testing 4.2 ~ One-Sample and Two-Sample z Tests 4.3 ~ Errors and Misinterpretations of Hypothesis Testing |
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| Chapter 5: Topics in Hypothesis Testing (31pp, v3.00, posted 8/9) | 5.1 ~ The t Distribution and t Tests 5.2 ~ The χ2 Distribution and χ2 Tests |
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| Exam Information | ||||
|---|---|---|---|---|
| Exams will be distributed in person during the course lecture period. Midterm exams are 90 minutes, while the comprehensive final is 2 hours and the short final is 1 hour. | ||||
| Exam | Date, Time, Location | Topics | Review Material | |
| Exam 1 (Form A), (sols) (Form B), (sols) |
Mon, Jul 25th In lecture |
WeBWorKs 1-3 Notes §1.1-1.4 + §2.1-2.2 |
Exam 1 Review Problems (answers) Review session Sat Jul 23rd, 1pm-3pm |
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| Exam 2 (Form A), (sols) (Form B), (sols) |
Mon, Aug 15th In lecture |
WeBWorKs 4-6 Notes §2.3 + 3.1-3.3 + 4.1-4.3 |
Exam 2 Review Problems (answers) Review session Sat Aug 13th, 1pm-3pm |
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| Final | Tue, Aug 23rd 10:30am-12:30pm Comp: Churchill 101 Short: Churchill 103 |
Comprehensive: WeBWorKs 1-7 Notes §1.1-5.2 |
Short: WeBWorK 7 Notes §5.1-5.2 |
Short-Final Review Problems (answers) Review sessions Sat Aug 20th + Sun Aug 21st, 1pm-3pm |
| For exams, you are permitted one "cheat sheet", consisting of a double-sided 8.5in-by-11in piece of paper. Calculators are permitted, but 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 |
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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 generally similar in style and difficulty to WeBWorK problems, but often feel harder because of the limited time and the fact that you do not have multiple attempts on the exam! | ||
| 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 July 4 (class starts 7/5) |
§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 7/10 at 5am Eastern. |
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| Week of July 11 | §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 Saturday 7/16 at 5am Eastern. |
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| Week of July 18 | §2.1.5: Independence §2.1.6: Covariance and Correlation §2.2: Continuous Random Variables §2.3.1: The Normal Distribution §2.3.2: The Central Limit Theorem Review for Exam 1 WeBWorK 3 due Saturday 7/23 at 5am Eastern. |
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| Week of July 25 |
EXAM 1 in class on Monday, July 25th §2.3.3: The Poisson Distribution and Poisson Limit Theorem §2.3.4: The Exponential Distribution and Memoryless Processes §3.1.1: Maximum Likelihood Estimates §3.1.2: Biased and Unbiased Estimators WeBWorK 4 due Saturday 7/30 at 5am Eastern. |
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| Week of August 1 | §3.1.3: Efficiency of Estimators §3.2.1: Confidence Intervals §3.2.2: Normal Confidence Intervals §4.1: Hypothesis Testing §4.2.1: One-Sample z Tests §4.2.2: Two-Sample z Tests WeBWorK 5 due Saturday 8/6 at 5am Eastern. |
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| Week of August 8 | §4.2.3: z Tests for Unknown Proportion §4.3.1: Type I and Type II Errors §4.3.2: Misinterpretations and Misuses of Hypothesis Testing §5.1.1: The t Distributions §5.1.2: Confidence Intervals Using t Statistics §5.1.3: One-Sample t Tests WeBWorK 6 due Saturday 8/13 at 5am Eastern. Review for Exam 2 |
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| Week of August 15 (class ends 8/18) |
EXAM 2 in class on Monday, August 15th §5.1.4: Two-Sample t Tests §5.1.5: Robustness of t Tests §5.2.1: The χ2 Distributions §5.2.2: χ2 Confidence Intervals and Hypothesis Tests §5.2.3: The χ2 Test for Independence §5.2.4: The χ2 Test for Goodness of Fit WeBWorK 7 due Saturday 8/20 at 5am Eastern. Review for Final Exam |
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| Week of August 22 |
FINAL EXAM Tuesday, August 23rd, 10:30am-12:30pm, Churchill 101 (Comprehensive) / 103 (Short) | ||