2019 November 30,

Math 265: Probability

Carleton College, Fall 2019, Joshua R. Davis, , CMC 324, x4095


Probability is a beautiful subject of pure mathematics. It is the theoretical basis for statistics. It finds heavy use in physics, computer science, and other scientific fields. And there's gambling.

This is a first course in probability. Approximately half of the course is discrete and the other half continuous. The prerequisites are Math 120 or Math 211. Talk to me if you are concerned about your background.

The course materials are

Our class meets in CMC 206 during period 5A (MonWed 1:50-3:00, Fri 2:20-3:20). My revised office hours are

No appointment is needed during office hours; just drop in. If you can't make office hours, then consult my schedule and e-mail me a couple of possible meeting times.


Final grades (A, B, etc.) are assigned according to an approximate curving process. I mean that there are no predetermined percentages (90%, 80%, etc.) required for specific grades. The advantage of this system is that student grades don't suffer when I write a difficult exam. The disadvantage is that you cannot compute your own grade. Visit me in my office, if you want me to estimate your current grade for you. The following elements contribute.

You are expected to spend about 10 hours per week on this course outside class. Some students need to spend more than 10 hours. If you find yourself spending more than 15 hours, then talk to me.

Standards for Work

On homework, you are encouraged to figure out the problems with other students. However, you should always write/type your solutions individually, in your own words. You may not copy someone else's work or allow them to copy yours. Presenting someone else's work as your own is a violation of Carleton's Academic Integrity standards.

Writing is not just for English and history majors. Written and oral communication skills are essential to every academic discipline and are highly prized by employers. In this course, your written work is evaluated both for correctness and for presentation.

Although homework is assigned every day, it is collected only once a week. When handing in a week's homework, staple your pages into a single packet, in the correct order. Multi-sheet packets that are not stapled are unacceptable. I will not accept packets that are not stapled. Is there a stapler in the classroom? Often not, so staple ahead of time. Is a paper clip okay? No.

Depending on time constraints in any given week, perhaps not all of your homework will be graded. In order to ensure full credit, do all of the assigned problems.

Special Accommodations

During the term, you have one free pass to hand in a week's homework packet late, no questions asked. Simply hand in your late packet when the next packet is due, writing "Late Pass Used" prominently at the top of the late packet.

Once you have used your late pass, no late assignments are accepted, except in extreme circumstances that typically involve interventions by physicians or deans.

If some medical condition affects your participation in class or your taking of exams, let me know in the first week of class. You may need to make official arrangements with the Disability Services.


This schedule is tentative. It is adjusted as we go along.

To help you decode the schedule, here is an example. On Day 01 we discuss basic concepts and counting strategies. Sections 1.1-1.4 of the textbook cover that material; read them before or after class, to get another treatment. You have homework called "Day 01", some of which is due on Day 01 and some of which is due on Day 02. If you wish, you can view and run the file games.R that I might have used in class.

M 09/1601basic concepts, countingDay 0101, 021.1-1.4games.R
W 09/1802counting, birthdayDay 02031.4-1.6birthday.R
F 09/2003birthday, replacement1.9 #24, 25, 41, 58061.7replacement.R
M 09/2304conditional probability, BayesDay 04062.1-2.3
W 09/2505independenceDay 05062.4-2.8montyHall.R
F 09/2706random variables, Bernoulli3.12 #1, 2, 6, 7093.1-3.3
M 09/3007geometric, binomialDay 07093.3, 4.3
W 10/0208lab, hypergeometric, negative binomialtutorial A-H123.4, 4.3tutorial.R
F 10/0409functions of random variables, CDFsDay 09123.5-3.7
M 10/0710independence, expectation3.12 #42, 43, 44ab; 4.12 #3b, 4123.8, 4.1-4.2vectorsPowerBall.R
W 10/0911Exam A
F 10/1112unconscious statistician, variance4.12 #14, 34, 47, 58, 59154.4-4.6
M 10/1413PoissonDay 13154.7-4.8poisson.pdf
W 10/1614continuous random variables5.10 #7, 8, 9155.1-5.2
F 10/1815exponential, Poisson processesDay 15175.5-5.6poissonProcess.R
M 10/21Midterm Break
W 10/2316normal5.10 #21, 22b, 23175.4
F 10/2517joint, marginal distributionsDay 17207.1
M 10/2818conditional distributions, independence7.8 #7e, 32, 35207.2
W 10/3019covariance, correlationDay 19237.3
F 11/0120transformations, convolutionDay 20238.1
M 11/0421transformations, change of variables8.9 #13, 14238.2
W 11/0622Exam B
F 11/0823conditional expectationDay 23269.1-9.3
M 11/1124moments, moment generating functionsDay 24266.1, 6.2, 6.4
W 11/1325inequalities, law of large numbersDay 252810.1-10.2
F 11/1526central limit theoremDay 262810.3clt.R
M 11/1827Monte Carlo methodsmonteCarlo.R #A, B, C, D28monteCarlo.R
W 11/2028Monte Carlo, review
S 11/23Exam C 8:30AM-11:00AM