Spring 2025 MA/STAT 416 - Probability
Sections 005 & 006
Welcome to the course homepage for Spring 2024 MA/STAT 416 sections 15620 and 15625 with Professor Eric Samperton. This webpage is our syllabus, so please read the whole thing.
- Location: LILY 3410
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Schedule:
- Section 005 (CRN 15620): MWF 3:30-4:20pm
- Section 006 (CRN 15625): MWF 2:30-3:20pm
- Midterm Exam 1 schedule: In-class on 2/17.
- Midterm Exam 2 schedule: In-class on 4/7.
- Final exam schedule: Thursday, 5/8, 08:00am - 10:00am, in LILY G126 (Note the different room!)
- Course homepage and syllabus: https://www.math.purdue.edu/~esampert/416/
- Detailed course calendar: https://www.math.purdue.edu/~esampert/416/cal
- Gradebook, announcements, and Boilercast streams & recordings are handled via Brightspace (Purdue login required): https://purdue.brightspace.com/d2l/home/1222859
- Instructor: Eric Samperton
- Email: my first name followed by AT purdue.edu
- Office: MATH 706 (go left when you exit the elevator)
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Office hours:
- Mondays 4:30-5:30pm
- Thursdays 7:00-8:00pm. This office hour will be virtual. Please see Brightspace for the Zoom link.
- Fridays: 1:15-2:15pm
- Stats Help Room: there is a drop-in help room maintained by the Statistics Department. Click here and scroll down to see the schedule.
Content
An introduction to mathematical probability suitable as a preparation for actuarial science, statistical theory, and mathematical modeling. General probability rules, conditional probability and Bayes's theorem, discrete and continuous random variables, joint and conditional distributions, standard discrete and continuous distributions and their properties, law of large numbers and central limit theorem. 3 credit hours
By the end of the semester, a successful student will be able to answer all of the following questions:
- What are the formal properties of any random system?
- How should probabilities be updated in light of new evidence?
- What are several different important examples of discrete and continuous random systems, and what are their properties?
- How do we make precise mathematics out of various intuitive ideas such as "expected value", "variance", "covariance" and the "Law of Large Numbers"?
- Why are some types of random systems (like bell curves) so prevalent throughout science?
Prerequisites
Multi-variable calculus is a prerequisite for this class. More precisely, you must have met one of the following minimal conditions: (Undergraduate level MA 26100 Minimum Grade of C- or Undergraduate level MA 17200 Minimum Grade of C- or Undergraduate level MA 26300 Minimum Grade of C-) or (Undergraduate level MA 17400 Minimum Grade of C- or Undergraduate level MATH 26100 Minimum Grade of C-) or Undergraduate level MA 18200 Minimum Grade of C- or Undergraduate level MA 27100 Minimum Grade of C- or Undergraduate level MA 27101 Minimum Grade of C-.
Reading
The required course textbook is A First Course in Probability (10th edition) by Sheldon Ross. The publisher is Pearson and the ISBN is 9780134753119. There is a reserve copy available in the math library. You can opt for an electronic copy of the book if you want, but note that we will not be using MyLab for homework.
Let me reiterate that the textbook is REQUIRED. I plan to assign homework problems from it and you are expected to keep up with the assigned course reading, which you can find on the detailed course calendar page.
Grading
Your final course grade will be determined by the following four categories of assignments:
- Daily in-class draft.
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Click here for rules
- At the end of each class, I will announce a single "draft problem".
- You must solve it on your own before the next class.
- At the beginning of the next class, I will perform a random "draft". To this end, I will randomly order all of the registered students for the class who are "draft eligble" (meaning they have not already been drafted on a previous day), and go down that day's ordered list one by one until I identify the first person who does not opt to "skip" being selected that day. The first student to meet these criteria will be the draftee for that day, which means they agree to present the solution to the draft problem at the chalkboard. The draft will be subject to the following constraints:
- Every student has 3 free skips.
- If a student is not present in class on a day when their name comes up in that day's draft, then they must utilize a skip.
- If a student uses their 3 free skips, then the use of any additional skips will result in 0 points toward their in-class draft score and they will no longer be draft eligible.
- The day's draftee will be given a score between 1 and 3 points for the quality of their presented solution.
- 1 point for trying at all.
- 2 points for a correct and clear solution.
- 3 points for a correct and clear solution presented in less than 3 minutes.
- The final potential draftee on any given day does not get to skip. They may only agree to present a solution or else take a 0 for their in-class draft. (It is likely that this rule will not ever need to be invoked.)
- Every student shall present exactly one solution after which they will no longer be draft eligible, or else earn 0 points.
- In the event that there are not enough days of class for all students to have an opportunity to present, there will be "make-up" days where multiple students will be allowed to present several different problems (which will be announced in advance, as usual).
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Click here for some notes
- While attendance in class is not mandatory, if you miss so many days of class that you must utilize more than 3 skips, then you will not be able to earn any of the 3 points.
- With enough notification or documentation, I am amenable to providing additional skips due to sickness, emergencies, or other worthwhile reasons. The best way to be sure that a skip will be provided is to email me before you expect to need to skip.
- Draft problems will be easier at the beginning of the semester, so get started with good habits pronto.
- Even if you are no longer draft eligble, you should still do the draft problem. It is good practice.
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- Homework. I will aim to assign homework every week, for a total of roughly 13 assignments. Homework will be posted on the detailed course calendar page. Assignments will generally be due in person at the beginning of class on Fridays. Your lowest two scores will be dropped. Each assignment will have approximately 6 problems on it. Late assignments will not be accepted.
- Two in-class midterm exams. They will be 50 minutes long. MT1 will happen on 2/17 and focus on material from chapters 1-3 of Ross. MT2 will happen on 4/7and focus on material froms chapters 4 and 5.
- Final exam. The in-class final will be 2 hours long. The final will be comprehensive, and include material from chapters 6, 7 and (possibly) 8. I will send more info about the schedule after the registrar finishes scheduling finals for the semester.
Your final course raw score will be computed using the following weights:
| Draft | 3% |
| Homework | 30% |
| Midterm 1 | 16% |
| Midterm 2 | 16% |
| Final exam | 35% |
Individual assignments will not receive letter grades or curves. Final course letter grades will be computed using a scale that is at least as generous as the usual 10 point scale.
Click to see usual 10 point grading scale
| >=97% | A+ |
| 93%-97% | A |
| 90%-92.99% | A- |
| 87%-89.99% | B+ |
| 83%-86.99% | B |
| 80%-82.99% | B- |
| 77%-79.99% | C+ |
| 73%-76.99% | C |
| 70%-72.99% | C- |
| 67%-69.99% | D+ |
| 63%-66.99% | D |
| 60%-62.99% | D- |
| <60% | F |
Please try to resolve any grading issues within one week after the return of the graded work.
Attendance
Regular attendance is expected but not mandatory except as far as the rules of the in-class draft are concerned (see above), and the fact that you are required to come to class on the dates of the exams. If you are sick, then for the consideration of your peers, please consider either watching the Boilercast live-stream from the comfort of your home (recordings can also be watched on your own) or else masking.
Academic integrity
Homework. When it comes to solving homework problems, an information source is generally allowed if it is legal, free, public, and passive. Legal means that your access to the information does not involve the violation of any law (e.g. copyright law); free means you do not pay for the information (the required textbook is the only exception to this policy); public means the information is available to any Purdue student without having to create an account or register for a service that is not provided by Purdue; and passive means that the information is prerecorded and not created in response to your input.
The use of almost any calculator or computer program is disallowed a priori, as it fails to meet the "passive" requirement. However, common programs such as a TI-87 calculator, MatLab or GeoGebra that do not use AI are exempted from this. If you are unsure if a specific computer program is allowed, please ask Professor Samperton.
Similarly, the use of other people is generally disallowed when it comes to getting help on homework problems, since asking another person a question fails to generate an answer in the form of passive information. However, any individual that is officially associated with this course (that is, your instructor, your classmates and any staff in the Stats Help Room) is exempt from this.
In fact, you are encouraged to collaborate with your classmates when solving homework problems, and you are generally welcome to use any textbooks, research papers, or other notes to solve homework problems, as long as the sources are legal, free, public and passive as explained above. However, you must use your own words and understanding when writing up your solutions (you can not just copy or quote), and you must cite any sources you use.
Examples of allowed resources: textbooks from the Purdue library; answers to questions that you yourself did not post on public online discussion forums such as Math Stack Exchange; publicly available YouTube videos. Of course, the use of any such source must be accompanied with a proper citation.
Examples of disallowed resources: typing a homework question directly into an online search engine or artificial intelligence program such as ChatGPT or WolframAlpha; posting a homework question on a forum such as StackOverflow or Chegg.
Violation of these expectations will typically result in a 0 for the offending assignment and the filing of an Academic Dishonesty Report with the Office of Student Rights and Responsibilities.
Finally, the use of "homework help services" (that is, professional cheating companies) such as Chegg, CourseHero, etc, is disallowed for help on any homework problems unless I give you my explicit permission. Any un-authorized use I discover will result in an F for the course and the filing of an Academic Dishonesty Report.
General studying. All of the above also applies when it comes to studying the recommended practice problems for the exams. However, for other studying, you are free to use whatever technologies or people you want as long as you do not violate the other policies. For example, if you want to use an AI to create a summary of your textbook and self-written homework solutions, then have at it. Of course, you should also feel free to talk to whomever you want about probability generally (just not the specifics of assigned problems if they are not in our class).
Exams. The in-class midterm and final exams are of course not to be done in collaboration with anyone. They will be closed-notes and closed-book, although I expect to provide you an officially sanctioned "cheat sheet." More info will be forthcoming as the first exam approaches.Communication
Professor Samperton's preferred modes of communication, in order of preference: talk to him before or after class > talk to him in office hours > send him an email > call his office phone at 41937. Don't send me messages on Brightspace, as I won't see those.
Brightspace
Most course materials will be hosted on the detailed course calendar page. However Brightspace will be used to send course announcements, host the Boilercast livestream and recordings, and handle the gradebook.
Privacy
All of the regularly scheduled course meetings will be recorded and made available for viewing by your classmates on Brightspace. If you have privacy concerns, please let me know.
Accessibility
Purdue University strives to make learning experiences accessible to all participants. If you anticipate or experience physical or academic barriers based on disability, you are encouraged to contact the Disability Resource Center at: drc@purdue.edu or by phone: 765-494-1247, as soon as possible.
If the Disability Resource Center (DRC) has determined reasonable accommodations that you would like to utilize in this class, you must send your Course Accommodation Letter to the instructor. Instructions on sharing your Course Accommodation Letter can be found by visiting: https://www.purdue.edu/drc/students/course-accommodation-letter.php. Additionally, you are strongly encouraged to contact the instructor as soon as possible to discuss implementation of your accommodations.
Non-discrimination statement
Purdue University is committed to maintaining a community that recognizes and values the inherent worth and dignity of every person; fosters tolerance, sensitivity, understanding, and mutual respect among its members; and encourages each individual to strive to reach his or her potential. In pursuit of its goal of academic excellence, the University seeks to develop and nurture diversity. The University believes that diversity among its many members strengthens the institution, stimulates creativity, promotes the exchange of ideas, and enriches campus life. See Purdue's full Nondiscrimination Policy Statement.
Other boilerplate
In extraordinary circumstances, this syllabus may be amended or changed as necessary in order to facilitate fair learning and grading. Any changes will be announced well in advance both in class and via Brightspace announcements.