Instructor: Tim Chumley
Office: Clapp 404b
Phone: 538-2299
e-mail: tchumley
Office Hours: Mondays 4:00–5:00, Tuesdays 12:00–1:00, Wednesdays 3:00–4:00, Thursdays 3:00–4:00, Fridays 1:00–2:00, and by appointment

Textbook: Probability with Applications and R, by Robert P. Dobrow, ISBN: 978-1118241257;
available as a free e-text


Announcements will be posted here throughout the semester.

Dec 11: The central limit theorem gives a way of characterizing the distribution of an i.i.d. sum of random variables. It shows how the normal distribution (whose density is the celebrated bell curve) arises as the distribution of a sum as the number of terms increases, regardless of what the distribution of the terms. Here are two demonstrations: one for the uniform distribution, and one for the exponential distribution.

Sep 25: I’ve updated the date of our first exam to October 11. This should let us resolve some conflicts with the Grace Hopper conference which some of you are attending. It will also give us some more time to digest material that will be on the exam. The caveat is that this is the day we return from fall break, but I hope this will let everyone study in a relaxed manner during that weekend. We’ll hold a review day in class the Friday before.

Sep 18: I thought I’d bring to everyone’s attention the website Lathisms, where every day at midnight between September 15th and October 15th (Hispanic Heritage Month), a prominent Latin@/Hispanic mathematician of the day is being featured and honored. Whether or not you identify as Latin@/Hispanic, I hope you find some inspiration in the calendar. Like many scientific fields, diversity is an issue in math that needs to be addressed, and hopefully this calendar either brings to attention some role models or inspires similar projects in the future. By the way, one of the creators of the site, Gabriel Sosa, is a visitor (and very nice guy) at Amherst College.

Sep 16: I have to change my office hour this coming Friday, September 22, to 10:00–11:00.

Sep 15: I’ve set a date for Quiz 1 below. An announcement will be made in class too.

Sep 11: I’ve added a Friday office hour. For now, it’s 1:00–2:00.

Sep 9: I’ve made an adjustment to Tuesday office hours and moved them to 12:00–1:00.


Check the syllabus for all the important class policies (grades, attendance, etc.).


There will be weekly homework assignments throughout the semester to be turned in, as well as suggested problems to be considered as additional practice.

  • Written assignments. A selection of problems taken from the textbook or other sources will be assigned to be due Fridays at 5pm.
    • These assignments are given so that you can practice writing mathematics and receive feedback on your progress.
    • If you would like feedback on a particular step in a problem, then you can indicate this on your assignment.
    • Each problem will be given a score out of 5. A score of 1 will be given to indicate that to stay on track you should get help from your instructor.
    • Please refer to these guidelines when writing your homework.
  • Submitting to Gradescope. We’ll be using an online submission tool called Gradescope to collect, grade, and return homework. Here are some notes:
    • Begin by signing up as a student on the Gradescope home page with Entry Code 9N88Y8.
    • The first step to submit your homework is scanning it and making a PDF. You can use a smartphone app or one of the public copy machines in places like the library.
    • Gradescope has made a guide to help with scanning and submitting.
    • More information is available in this general help guide.
    • Please let me know of any issues that come up!
  • Suggested problems. The book has a good variety of problems, both in terms of content and difficulty level. As you study throughout the semester, you might consider browsing and trying the problems at the end of the chapter for extra practice. I’ll always be happy to help over email or in office hours if you’re stuck.
Assignment Due
Problem set 0 Sep 11
Problem set 1 (solutions) Sep 15
DataCamp tutorial Sep 18
Problem set 2 (hints) (solutions) Sep 22
Problem set 3 (hints) (solutions) Sep 29
Problem set 4 (solutions) Oct 6
Problem set 5 (solutions) Oct 20
Problem set 6 (solutions) Oct 27
Problem set 7 (solutions) Nov 3
Problem set 8 (solutions) Nov 10
Problem set 9 (solutions) Dec 1
Problem set 10 (solutions) Dec 8


There will be a few quizzes during the semester—roughly 2-3 total, one midway between each exam. These are intended to break up the material between exams and get everyone studying. The precise sections covered will be listed below and the types of problems will be discussed in class.

Quiz Date Material Solutions
Quiz 1 Sep 25 Chapter 1, 2.1, 2.3 (pdf)
Quiz 2 Oct 30 3.5, 3.7, 4.1 – 4.6 (pdf)
Quiz 3 Dec 4 6.1 – 6.5 (pdf)


There will be three exams:

Exam Date Time and Location Material Study material Solutions
Exam 1 Oct 11 in class Chapters 1, 2, 3.1-3.4 review guide (solutions) (pdf)
Exam 2 Nov 15 in class 3.5, 3.7, 4.1-4.6, 5.1-5.3 review guide (solutions) (pdf)
Final Dec 15 - 19 self-scheduled 6.1-6.8, 6.10, 4.8, 8.1, 8.3 review guide (solutions) (pdf)

Course plan

Our plan is to cover the textbook chapters 1-4, 6, and parts of 5, 7, 8, and 9. Below is a rough outline of what is to be covered week by week through the semester. Please check back regularly for precise details on what is covered, as well as postings of in-class worksheets and other activities. Also note that the days of the week under Sections in the table below provide links to class notes.

Week Sections In-class activities Problems
Sep 4 - Sep 8 Wednesday: 1.1, 1.2
Friday: 1.3, 1.4
Sample spaces 1.1, 1.2, 1.6, 1.8,
1.9, 1.10, 1.11, 1.20, 1.22, 1.28
Sep 11 - Sep 15 Monday: 1.5, 1.6, 1.10
Wednesday: 1.8, 1.9
Friday: 1.7
Monte Carlo simulation (markdown)
Counting (solutions)
1.16, 1.30, 1.44,
1.18, 1.24, 1.31
Sep 18 - Sep 22 Monday: 2.1, 2.3
Wednesday: 2.4, 2.5
Friday: 2.4, 2.5
Conditioning (solution)
Law of total probability & Bayes formula
2.2, 2.5, 2.8, 2.10, 2.12
2.14, 2.16a, 2.22,
2.24, 2.26, 2.28
Sep 25 - Sep 29 Monday: 3.1
Wednesday: 3.2, 3.3
Friday: 3.4

Counting II (solutions)
3.1, 3.2, 3.3
3.7, 3.9
3.12, 3.14, 3.16abcde, 3.22
Oct 2 - Oct 6 Monday: 3.5
Wednesday: 3.7
Friday: review
Binomial distribution in R, Examples (solutions)
3.23e, 3.24, 3.26
3.30ab, 3.34, 3.36
Oct 9 - Oct 13 Monday: fall break
Wednesday: exam
Friday: 4.1, 4.2

Scrabble, PMF & Expectation

4.2, 4.3, 4.4
Oct 16 - Oct 20 Monday: 4.2, 4.3, 4.4
Wednesday: 4.4, 4.5
Friday: 4.6
Joint PMF 4.12, 4.18, 4.19
4.6, 4.22, 4.23
4.24, 4.26, 4.29
Oct 23 - Oct 27 Monday: 4.4, 5.1 – 5.2
Wednesday: 5.1, 5.2 continued
Friday: 5.3, Chapter 5 overview

Coupon collector, Problem of points, Simulation
Summary of distributions, Comparing distributions
4.32, 5.4, 5.5, 5.11, 5.15
5.6, 5.17
5.32, 5.34, 5.35
Oct 30 - Nov 3 Monday: 6.1
Wednesday: 6.2
Friday: 6.3, 6.4
Probability density function,
and cumulative distribution function
6.1, 6.2, 6.9
6.3, 6.5, 6.6
6.8, 6.11
Nov 6 - Nov 10 Monday: 6.5
Wednesday: 6.6
Friday: 6.6 continued
Exponential distribution
Functions of random variables reading
Functions of random variables worksheet
R code
6.12, 6.20, 6.21
6.22, 6.23, 6.24
Nov 13 - Nov 17 Monday: review
Wednesday: exam
Friday: 6.7

Joint densities

6.30, 6.31, 6.32
Nov 20 - Nov 24 Monday: 6.7 continued
Wednesday: break
Friday: break
Nov 27 - Dec 1 Monday: 6.8, 6.10
Wednesday: 6.10, 4.8
Friday: 4.8, 8.3
Independence of continuous random variables 6.38, 6.41, 6.51
6.42, 4.46, 4.48
Dec 4 - Dec 8 Monday: 8.3
Wednesday: 8.1
Friday: 8.1

Conditional densities
8.10, 8.14, 8.17
8.1, 8.3, 8.4
Dec 11 - Dec 15 Review

Getting help

Here’s a few ways to get help:

  • Office hours (listed at the top of this page). These are times I hold on my schedule to be available for students. I like to use these times as open drop in sessions where there may be multiple students getting help simultaneously, but it’s expected that you come with specific questions about notes, homework problems, or the text that you have thought about already. If you need to schedule a time to meet with me one-on-one, either to discuss something private or because you can’t make my office hours, please send me an email with times that you are available to meet, and I will find a time that works for both of us.
  • Study groups. I strongly encourage you to form small groups and work together on problems. My advice though is to try problems by yourself before discussing them. We have several spaces on the fourth floor of Clapp where students can work together for extended periods of time.


  • Everyone will be invited to join DataCamp, which provides an introductory R tutorial. It’s a convenient way to gain some familiarity with R, a useful tool for our course and beyond. Let me know if you have any trouble with the invitation or need some help with the material in the tutorial.

  • Our textbook has a useful collection of R scripts available here; contained there are all the R code snippets you’ll notice interspersed in the text.