Instructor: Tim Chumley
Office: Clapp 404b
Phone: 538-2299
e-mail: tchumley
Office Hours: Mondays 9:00-10:00, Tuesdays 1:00–2:00, Wednesdays 3:00–4:00, Thursdays 4:00–5:00, and by appointment

Textbook: Probability with Applications and R, by Robert P. Dobrow, ISBN: 978-1118241257;
available as a free e-text;
available on library reserve under QA276.45.R3 D63 2014


Announcements will be posted here throughout the semester.

Dec 7: We didn’t get to conditional densities (section 8.1), but here are some lecture notes and a worksheet if you’re interested.

Past announcements

Oct 15: Like I mentioned in class, the average score on the exam was an 88%, the median was 90%, and they went well overall. I am happy to talk over questions one-on-one with everyone, whether it’s about some technical details, grading decisions, or anything else.

Here are some comments about revisions. If you lost half or more points on a problem, you can earn back some credit by doing the following:

  1. Try to redo the problem on your own or with my help.
  2. Write a sentence or two explaining what went wrong the first time (bad interpretation, didn’t know a theorem, etc).
  3. Come see me after 1 and 2 and then we can talk and I’ll give another problem like it to check if the concept has been learned.

Please finish steps 1 and 2 by next Monday and step 3 by the following Wednesday. I also want the process to be clear and fair for everyone. Students who have the chance to do revisions won’t end up with higher grades than those who don’t, but I want everyone to be aware of the policy.

Oct 14: For this week, Faryal’s evening help will be in Reese 307 on Tuesday from 7 to 9 pm.

Sep 21: Please complete the following online assignment before class on Monday, September 24.

Sep 17: There were more great questions this week. I’m posting some responses here and will also discuss some in class.

Sep 14: Two announcements:

  • It turns out that for an overwhelming majority of the class, Sundays work much better for evening help, so we’ll be moving our sessions to Sundays, 7-9pm in Clapp 401. Thanks for replying to the survey yesterday!
  • Please complete the following online assignment before class on Monday, September 17.

Sep 13: Please fill out the evening help availability form.

Sep 12: You’ve asked great questions in the online assignment over the weekend! I’m posting some responses here.

Sep 8: A few announcements:

  • I’ve made a Google Group for our class. Please make sure you join in order to receive emails from me with important announcements.
  • Please complete the following online assignment before class on Monday, September 10.


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 Wednesdays in class.
    • 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 steps 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 read these guidelines for writing up your homework solutions.
  • 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.
  • Collaboration. I want you to work together on the written homework; the process of explaining your ideas to one another really helps in learning math. However, you must write up the problems on your own, listing the people with whom you worked on the problems. Please acknowledge any source of help, including classmates or outside texts, by writing “help from …” at the top of your assignment. Also, please only write what you understand so that I know where to help.
Assignment Due
Homework 0 Sep 7
Homework 1 (solutions) Sep 12
Homework 2 (solutions) Sep 19
Homework 3 (solutions) Sep 26
Homework 4 (solutions) Oct 3
Homework 5 (solutions) Oct 17
Homework 6 (solutions) Oct 24
Homework 7 (solutions) Oct 31
Homework 8 (solutions) Nov 7
Homework 9 (solutions) Nov 19
Homework 10 (solutions) Nov 28
Homework 11 (solutions) Dec 5


There will be a few quizzes during the semester. There will be some short (5-10 minute) self-check quizzes on Mondays with straightforward questions (for example, stating a definition). They are written to make sure you’re comfortable with the basics. These will be counted toward the participation part of your grade. There will be some longer (15-20 minutes) quizzes on Fridays with problems similar to homework. These are intended to break up the material between exams and get everyone studying. The quizzes will be announced below with some advance notice.

Quiz Date Material Solutions
Quiz 1 Sep 14 1.1 - 1.6 (pdf)
Quiz 2 Sep 28 1.7, Ch. 2 (pdf)
Quiz 3 Oct 5 Ch. 3, 4.1 - 4.2 (pdf)
Quiz 4 Oct 26 5.1, 5.2, 6.1, 6.2 (pdf)
Quiz 5 Nov 2 6.4, 6.5, 6.7 (pdf)
Quiz 6 Nov 9 6.7, 6.8, 6.10 (pdf)
Quiz 7 Nov 30 9.1 - 9.4 (pdf)
Quiz 8 Dec 10 9.5, 4.8, 8.3 (pdf)


There will be three exams. The dates for the two mid-terms are subject to change slightly:

Exam Date Time and Location Material Study material
Exam 1 Oct 12 in class 1.1 - 4.6 review guide (solutions)
Exam 2 Nov 16 in class 5.1 - 7.1 review guide (solutions)
Final Dec 14 - 18 self-scheduled cumulative review guide (solutions)

Course plan

Our plan is to cover most of chapters 1-4, 6, and parts of chapters 5, 7, 8, and 9 in the textbook. 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 3 – Sep 7 Wednesday: 1.1 - 1.4
Friday: 1.4, RStudio introduction
First day worksheet
Introduction to R, Sets and probability functions
1.21, 1.22, 1.25
1.26, 1.33
Sep 10 – Sep 14 Monday: 1.5, 1.6
Wednesday: 1.7, 1.8
Friday: 1.10
Problem solving techniques
Intro to simulation
1.14, 1.15, 1.16
1.17, 1.29, 1.30, 1.39, 1.40
1.6, 1.24, 1.35, 1.36
Sep 17 – Sep 21 Monday: 2.1, 2.3
Wednesday: 2.4, 2.5
Friday: 3.4
Conditional probability
Law of total probability, Bayes’ rule
Counting subsets
2.8, 2.9, 2.13
2.18, 2.23, 2.24, 2.25, 2.26, 2.27
3.12a, 3.14, 3.18
Sep 24 – Sep 28 Monday: 3.1 - 3.3, 3.5
Wednesday: 3.5, 3.7
Friday: 3.7, 4.1
Binomial distribution
More on binomial distribution
Poisson distribution
3.7, 3.9, 3.21
3.22, 3.24a, 3.28
3.31, 3.33, 3.36
Oct 1 – Oct 5 Monday: 4.1, 4.2
Wednesday: 4.3, 4.5
Friday: 4.4, 4.6
Joint distributions
4.1, 4.4, 4.8
4.11, 4.12, 4.17, 4.19
4.25, 4.27, 4.29
Oct 8 – Oct 12 Monday: break
Wednesday: review
Friday: exam
Oct 15 – Oct 19 Monday: 5.1, 5.2
Wednesday: 6.1, 6.2
Friday: LEAP (no class)
Negative binomial distribution
Probability density functions
5.1, 5.4, 5.11
6.1, 6.2, 6.3
Oct 22 – Oct 26 Monday: 6.2, 6.4
Wednesday: 6.3, 6.5
Friday: multivariable calc review
CDF, expectation
Uniform, exponential distributions
Iterated integrals (solutions)
6.5, 6.6, 6.11
6.12, 6.14, 6.17, 6.18, 6.19
Oct 29 – Nov 2 Monday: 6.7
Wednesday: 6.7, 6.8
Friday: 6.10
Joint densities
Marginal densities, independence (solutions)
Min, max of independent random variables
6.30, 6.31, 6.32
6.34, 6.38, 6.51
6.41, 6.42, 6.52
Nov 5 – Nov 9 Monday: 7.1
Wednesday: 7.1
Friday: 9.1 - 9.3
Normal distribution
Sums of normal random variables
R code
7.1, 7.2, 7.3
7.4, 7.5, 7.6
7.10, 7.11, 7.12
Nov 12 – Nov 16 Monday: 9.3, 9.4
Wednesday: review
Friday: exam
Monte Carlo integration
Extra review (solutions)
9.9, 9.10, 9.11
Nov 19 – Nov 22 Monday: 9.4, 9.5
Wednesday: break
Friday: break
Central limit theorem
Nov 26 – Nov 30 Monday: 9.5
Wednesday: 9.5
Friday: 4.8
Moment generating functions (solution)
Continuity theorem
Discrete conditional distributions
Dec 3 – Dec 7 Monday: 8.3
Wednesday: homework discussion
Friday: 8.3
Conditional expectation

Review problems (solutions)
Dec 10 – Dec 14 Monday: wrap up
Wednesday: reading day
Friday: exam period begins
Extra review (solutions)

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.
  • Evening TA help. A student TA will hold office hours for the class one night a week in Clapp. These hours will be an opportunity for you to ask questions on homework and class material. You should also see this as a place where you can find classmates to work with on homework as a group. Faryal Usman is the official TA for our section. She will hold evening help on Sundays, 7:00 – 9:00 pm in Clapp 401.
  • 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.


  • 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.