Matthew L. Wright
Assistant Professor, St. Olaf College

Probability Theory

Math 262 ⋅ Fall 2016

Welcome to Probability Therory! For course info and policies, please see the syllabus. For grades, log into Moodle. If you need help or have questions, please contact Prof. Wright; office hours are Mon. 1:15–1:45 & 3–3:30, Wed. 9–10, Thurs. 10–11 & 1–2, Fri. 1:15–1:45 & 3–3:30, or by appointment in RMS 409.

Below is a tentative outline of the course. Use the controls at right to make the page easier to view.

Unless otherwise noted, homework listed below is due in the homework mailbox at 5:00pm on the due date.

September 5–9 − hide
DayTopicHomework Assigned
Friday
Sep. 9
Introduction
class notes

Complete the syllabus quiz by Monday, Sept. 12.

Read §1.1, Sample Spaces and Events, in the textbook. Then begin Homework 1 (due Wednesday, Sept. 14).

September 12–16 − hide
DayTopicHomework Assigned
Monday
Sep. 12
Axioms of probability
class notes
Read §1.2;
Finish Homework 1.
Wednesday
Sep. 14
Counting principles
class notes
Read §1.3;
Begin Homework 2 (due Monday, Sept. 19).
Friday
Sep. 16
Counting principles
class notes
Finish Homework 2.
September 19–23 − hide
DayTopicHomework Assigned
Monday
Sep. 19
Conditional probability
class notes
Read §1.4;
Begin Homework 3 (due Friday, Sept. 23).
Wednesday
Sep. 21
Bayes' Theorem and independence
class notes
Read §1.5;
Finish Homework 3.
Friday
Sep. 23
Simulation of random events
class notes
Read §1.6;
Begin Homework 4 (due Wednesday, Sept. 28).
September 26–30 − hide
DayTopicHomework Assigned
Monday
Sep. 26
Random variables and discrete distributions
class notes
Finish Homework 4.
Wednesday
Sep. 28
Expected value and standard deviation
class notes
Read §2.1 to §2.3;
Begin Homework 5.
Friday
Sep. 30
Probability problems
(Prof. Wright at conference, no office hours — sorry!)
Finish Homework 5.
October 3–7 − hide
DayTopicHomework Assigned
starMSCS Colloquium: Craig Westerland, Arithmetic Statistics (3:30pm in RNS 310)Monday
Oct. 3
Binomial distribution
class notes
Read §2.4;
Homework 6 due Wednesday
Wednesday
Oct. 5
Binomial and Poisson distributions
class notes
study for the exam
starMSCS Research Seminar: Matthew Richey, The Curious Case of 2s and 3s (3:40pm in RNS 204)Friday
Oct. 7

Exam 1:

  • This exam will cover Sections 1.1 through 1.5 and 2.1 through 2.4.
  • Calculators will be permitted, but probably not very helpful, and certainly not necessary.
  • Books, notes, and internet-capable devices will not be permitted during the exam.
  • A review page, with suggested problems, is avaible here.
October 10–14 − hide
DayTopicHomework Assigned
starMSCS Colloquium: Pamela Pierce, The Circle Squaring Problem: A Tale of Undergraduate Research (3:30pm in RNS 210)Monday
Oct. 10
Discrete distributions
class notes
Read §2.5;
Begin Homework 7.
Wednesday
Oct. 12
Discrete distributions
class notes
Read §2.6;
Finish Homework 7.
Friday
Oct. 14
Discrete distributions
class notes
Read §2.8
October 17–21 − hide
DayTopicHomework Assigned
Monday
Oct. 17
Fall Break — no class!
Wednesday
Oct. 19
Simulation of discrete random variables
and moment generating functions
class notes
Read §2.7;
Begin Homework 8.
starMSCS Research Seminar: Kristin Heysse, Spectral graph theory: a crossroads of graphs and matrices (3:40pm in RNS 204)Friday
Oct. 21
Moment generating functions
class notes
Re-read §2.7;
Finish Homework 8.
October 24–28 − hide
DayTopicHomework Assigned
Monday
Oct. 24
Continuous distributions
class notes
Read §3.1;
Begin Homework 9.
Wednesday
Oct. 26
Expected values and moment generating functions
class notes
Read §3.2;
Finish Homework 9.
Friday
Oct. 28
Normal distribution
class notes
Read §3.3;
Begin Homework 10
October 31 – November 4 − hide
DayTopicHomework Assigned
starMSCS Colloquium: St. Olaf CS students, What is Summer Research Like in Computer Science? (3:10pm in RNS 310)Monday
Oct. 31
Normal and exponential distributions
class notes
Read §3.4;
Finish Homework 10
Wednesday
Nov. 2
Exponential and gamma distributions
class notes
Read §3.4;
Begin Homework 11
starMSRS Research Seminar: Matthew Wright, Barcodes: Discerning the Shape of Data (3:40pm in RNS 204)Friday
Nov. 4
Transformations of a random variable
class notes
Read §3.7;
Finish Homework 11
November 7–11 − hide
DayTopicHomework Assigned
starMSCS Colloquium: Lyndsay Shand, Spatial Data: What is it and what can we do with it? (3:30pm in RNS 210)Monday
Nov. 7
Transformations and simulation
class notes
study for the exam
Wednesday
Nov. 9

Exam 2:

  • This exam will cover Chapters 2 and Sections 3.1 – 3.4 and 3.7.
  • The exam will consist of an in-class portion and a take-home portion.
  • For the in-class portion: books, notes, and internet-capable devices will not be permitted. Calculators will be permitted, but probably not very helpful, and certainly not necessary.
  • The take-home portion will be distributed on Nov. 9 and due at the beginning of class on Nov. 11. For this portion of the exam you may use your textbook, your notes, a calculator, R, and Mathematica, but not other people, web sites, books, etc. Remember the honor code!
  • Click here for more information and suggested review problems.
starMSRS Research Seminar: Matthew Wright, RIVET: Software for Topological Data Analysis (3:40pm in RNS 204)Friday
Nov. 11
Joint distributions
class notes
Read §4.1;
Begin Homework 12
November 14–18 − hide
DayTopicHomework Assigned
Monday
Nov. 14
Marginal distributions and expected values
class notes
Read §4.2;
Finish Homework 12
Wednesday
Nov. 16
Covariance, correlation, and linear combinations
class notes
Read §4.3;
Begin Homework 13
starMSRS Research Seminar: Stefanie Wang, Catalan and Peri-Catalan Numbers: Counting the Effects of Nonassociativity (3:40pm in RNS 204)Friday
Nov. 18
Linear combinations of random variables
class notes
Re-read §4.3;
Finish Homework 13
November 21–25 − hide
DayTopicHomework Assigned
Monday
Nov. 21
Linear combinations; conditional distributions
class notes
Read §4.4;
Begin Homework 14
Wednesday
Nov. 23
Thanksgiving Break — no class!
Friday
Nov. 25
Thanksgiving Break — no class!
November 28 – December 2 − hide
DayTopicHomework Assigned
Monday
Nov. 28
Conditional distributions and expectations
class notes
Finish Homework 14
Wednesday
Nov. 30
Limit theorems
class notes
Read §4.5;
Begin Homework 15 (due next Wednesday)
starMSRS Research Seminar: Jill Dietz, Automorphisms of Group Extensions (3:40pm in RNS 204)Friday
Dec. 2
Limit Theorems
class notes
Re-read §4.5;
Continue work on Homework 15
December 5–9 − hide
DayTopicHomework Assigned
starMSCS Colloquium: Steve Butler, An Introduction to the Mathematics of Juggling (3:30pm in RNS 310)Monday
Dec. 5
Law of Large Numbers and Distribution Function Method
class notes
Read §4.6;
Finish Homework 15
Wednesday
Dec. 7
Tramsformations of jointly distributed random variables
class notes
Re-read §4.6;
Begin Homework 16
Friday
Dec. 9
Order statistics
class notes
Read §4.9;
Finish Homework 16
December 12–16 − hide
DayTopic
Monday
Dec. 12
Review
class notes—solutions to in-class practice problems
Thursday
Dec. 15

Final Exam: 2:00 – 4:00pm

  • This exam will be cumulative, with emphasis on Chapter 4.
  • The exam will consist of an in-class portion and a short take-home portion.
  • The take-home portion will be distributed on Dec. 12 and due at the final exam time on Dec. 15. For this portion of the exam you may use your textbook, your notes, the course web site, a calculator, R, and Mathematica, but not other people, web sites, books, etc. Remember the honor code!
  • For the in-class portion: books, notes, and internet-capable devices will not be permitted. Calculators will be permitted, but probably not very helpful, and certainly not necessary.
  • Click here for more information and suggested review problems.
  • Here are some practice problems on transformations of random variables.
  • Lastly, make sure you are familiar with the St. Olaf final exam policies.