Probability Theory, Fall 2023
This page lists archived materials that are no longer in use. Please return to the home page for the current version of the course.
Instructor: Trevor Ruiz (he/him/his) [email]
Class meetings:
- [Section 01/3585] 4:10pm – 5:00pm MTWR Construction Innovations Center Room C201
- [Section 02/3430] 5:10pm – 6:00pm MTWR Construction Innovations Center Room C201
Office hours: 1:00pm – 3:00pm WR 25-236 and by appointment
Read the [course syllabus]
Week 0 (9/21/23)
Course introduction.
Class meetings
Thursday: course introduction [slides]
Assignments
Complete intake survey
Week 1 (9/25/23)
Sets and set operations; probability spaces; properties of probability.
Suggested reading
DG&S 1.4 — 1.6
Lecture notes
Class meetings
Monday: sets
Tuesday: sets, cont’d
Wednesday: probability spaces
Thursday: properties of probability measures
Assignment
Homework 1 due Thursday 10/5 [solutions]
Week 2 (10/2/23)
Probability on finite sample spaces; counting rules and applications.
Suggested reading
DG&S 1.7 — 1.10
Lecture notes
[counting]
Class meetings
Monday: wrap-up; probability on finite sample spaces
Tuesday: counting principles and multiplication rules
Wednesday: combinations and permutations
Thursday: combinations and permutations
Assignment
Homework 2 due Thursday 10/12 [solutions]
Week 3 (10/9/23)
Conditional probability; independence; Bayes’ theorem.
Suggested reading:
DG&S 2.1 — 2.3
Lecture notes
Class meetings:
Monday: conditional probability and basic properties
Tuesday: independence
Wednesday: Bayes’ theorem
Thursday: odds and conditional odds
Assignment
- Homework 3 due Thursday 10/19 [solutions]
Week 4 (10/16/23)
Gambler’s ruin; introduction to random variables; midterm review
Midterm study guide — check back for updates [solutions to practice problems]
Suggested reading:
DG&S 2.4
Lecture notes
Class meetings:
Monday: the gambler’s ruin problem
Tuesday: midterm review session
Wednesday: random variables
Thursday: Midterm 1 [solutions]
Assignment
- None — enjoy!
Week 5 (10/23/23)
Discrete and continuous random variables; characterizing probability distributions
Suggested reading:
DG&S 3.1 — 3.3
Lecture notes
Class meetings:
Monday: definition of a random variable; the CDF
Tuesday: discrete and continuous random variables
Wednesday: characterizing distributions
Thursday: common distributions
Assignment
- Homework 4 due Thursday 11/2 [solutions]
Week 6 (10/30/23)
Common families of probability distributions
Suggested reading:
This week lectures will cover a blend of material in DG&S 4.1 – 4.4 and 5.1 – 5.6, but some material in those sections is deferred until later sections.
Lecture notes
Class meetings:
Monday: probability distributions based on Bernoulli trials
Tuesday: expected value; common discrete and continuous distributions
Wednesday: the Gaussian/normal distribution
Thursday: moments; the moment generating function
Assignment
- Please fill out feedback survey by the end of the week
- Homework 5 due Thursday 11/9 [solutions]
Week 7 (11/6/23)
Moments and moment generating functions; the gamma distribution
Suggested reading
DG&S section 4.4, select material from sections 5.1 – 5.6, and section 5.7
Lecture notes
[moments]
Class meetings:
Monday: moments and moment generating functions
Tuesday: the gamma distribution
Wednesday: recap of common distributions and their properties
Thursday: practice problems
Assignment
- Homework 6 due Thursday 11/16 [solutions]
Week 8 (11/13/23)
Review of random variables and common distributions; expectation inequalities
Suggested reading:
Hogg & Craig section 1.8
Lecture notes
Class meetings:
Monday: review and practice problems
Tuesday: review and practice problems
Wednesday: expectation inequalities
Thursday: Midterm 2 in class [solutions]
Assignment
None; enjoy!
Week 9 (11/27/23)
Multivariate distributions and transformations
Suggested reading:
DG&S 3.4 –3.5
Lecture notes
Class meetings:
Monday: random vectors
Tuesday: joint distribution functions
Wednesday: transformations of continuous random vectors
Thursday: the sum of jointly uniform random variables on the unit square
Assignment
Midterm corrections due Thursday 11/30 Homework 7 due Thursday 12/7 [solutions]
Week 10 (12/4/23)
Covariance, correlation, independence, and conditional distributions
Lecture notes
Class meetings:
Monday: covariance and correlation
Tuesday: conditional distributions
Wednesday: independence
Thursday: wrapping up
Final exam week (12/11/23)
[final study guide] [final exam solutions]
Office hours
Tuesday: 1pm-3pm in 25-107G
Wednesday: 1pm-3pm in 25-107G
Final exams
Held in usual classroom (186-C201)
Section 1 Wednesday 12/13/23 4:10pm – 7pm
Section 2 Friday 12/15/23 4:10pm – 7pm