﻿ JRD: Math 265

2018 November 27,

# Math 265: Probability

Carleton College, Fall 2018, Joshua R. Davis, , CMC 324, x4095

## Introduction

Probability is a beautiful subject of pure mathematics with many applications throughout the sciences. It is the theoretical basis for statistics. It finds heavy use in quantum theory, thermodynamics, finance, traffic flow, meteorology, etc. 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

• Introduction to Probability by Blitzstein and Hwang. Starting this year, this text is used in most sections of Math 265.
• Here are the exams from this term, with quartiles (75th, 50th, and 25th percentiles).
• Here are the exams from my fall 2017 version of the course. The order of topics was somewhat different in that term, but they still might help you study in this course.

Our class meets in LDC 104 during period 5A (MonWed 1:50-3:00, Fri 2:20-3:20). My office hours are currently

• Monday 3:10-4:20 (6A),
• Tuesday 10:10-11:00,
• Wednesday 3:10-4:20 (6A),
• Thursday 9:30-10:20, 3:00-3:50.

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.

## Responsibilities

Final grades (A, B, etc.) are assigned according to an approximate curving process. By this 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.

• Participation: You are expected to attend every class meeting promptly, take notes, and participate in discussion and group work. You can make up for a deficiency in class participation by talking with me in office hours or generally demonstrating exceptional effort and interest. Participation is used to make small adjustments to the final course grade. Additionally, a requirement for passing this course is that you visit me in my office at least once during the first two weeks.
• Assignments: Homework assignments are the core of the course; they are where you learn the material. Altogether they count for 25% of your grade.
• Exam A: The first midterm exam is given in class about one third of the way through the course. It counts for 25% of your course grade.
• Exam B: The second midterm is given in class about two thirds of the way through the course. It counts for 25% of your grade.
• Exam C: The final exam is scheduled for Monday November 19 from 3:30 to 6:00. This exam counts for 25% of your course grade. Self-scheduled final exams are not allowed.

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.

## Schedule

To help you decode the schedule, here is an example. On Day 01 we discuss basic concepts and counting strategies. Sections 1.1-1.3 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 used in class.

M 09/1001basic concepts, countingDay 0101, 021.1-1.3games.R
W 09/1202counting, birthdayDay 02051.4-1.6birthday.R
F 09/1403birthday, replacement1.9 #24, 41, 58051.7replacement.R
M 09/1704conditional probabilityDay 04082.1-2.3
W 09/1905Bayes' theorem, independenceDay 05082.4-2.8montyHall.R
F 09/2106random variables, BernoulliDay 06083.1-3.3
M 09/2407geometric, binomialDay 07103.3, 4.3
W 09/2608lab, hypergeometric, negative binomialfinish tutorial103.4, 4.3tutorial.R
F 09/2809functions of random variables, CDFs3.12 #5, 6, 26143.5-3.7
M 10/0110independence, expectation3.12 #42, 43, 44ab, 4.12 #3b, 4143.8, 4.1-4.2
W 10/0311Exam A
F 10/0512unconscious statistician, variance4.12 #14, 34, 47, 58, 59144.4-4.6vectorsPowerBall.R
M 10/0813PoissonDay 13164.7-4.8poisson.pdf
W 10/1014continuous random variables5.10 #7, 8, 9165.1-5.2
F 10/1215exponential, Poisson processes5.10 #38, 40, 46, 48195.5-5.6
M 10/15Midterm Break
W 10/1716normal5.10 #21, 22, 24, 25, 26195.4
F 10/1917joint, marginal, conditional distributions7.8 #1, 4, 9, 16, 17197.1
M 10/2218covariance, correlation7.8 #7e, 32, 35, 40, 55217.2-7.3
W 10/2419transformations8.9 #1, 3, 11218.1
F 10/2620convolutions, etc.Day 20258.2
M 10/2921catching upDay 2125investment.R
W 10/3122Exam B
F 11/0223conditional expectationDay 23259.1-9.3
M 11/0524moments, moment generating functionsDay 24286.1, 6.4
W 11/0725inequalities, law of large numbersDay 252810.1-10.2
F 11/0926central limit theoremDay 262810.3clt.R
M 11/1227Monte Carlo methodsnonemonteCarlo.R
W 11/1428Monte Carlo, reviewnone
M 11/19Exam C 3:30PM-6:00PM