ORF 309 / EGR 309 / MAT 380  Spring 2018
Probability and Stochastic Systems
Basic info
Course description: This is an undergraduate introduction to probability and its applications. Topics include: basic principles of probability, lifetimes and reliability, Poisson processes, random walks, Brownian motion, branching processes, and Markov chains. The goal of the course is to teach you how to reason precisely about randomness and how to think probabilistically.
Prerequisites: MAT 201 or permission of the instructor.
Instructor: Miklos Z. Racz
Lecture time and location: MWF 11:00  11:50 am, 104 Computer Science
Office hours: W 9:00  11:00 am, 204 Sherrerd Hall (moves to 125 or 107 Sherrerd Hall in case of many students)
Teaching Assistants (AIs):
 Daniel Gitelman (Head AI), office hours: Th 8:00  10:00 pm, 005 Sherrerd;
 Stephen Chen, office hours: Tu 11:00 am  1:00 pm, 005 Sherrerd;
 Pierre Yves Gaudreau Lamarre, office hours: Th 2:00  4:00 pm, 005 Sherrerd;
 Guillaume Martinet, office hours: Th 6:00  8:00 pm, 005 Sherrerd;
 Kaizheng Wang, office hours: W 2:00  4:00 pm, 005 Sherrerd;
 Qingcan Wang, office hours: W 7:00  9:00 pm, 005 Sherrerd.
Precepts:
 P1: M 7:30  8:20 pm, EQuad 225; Guillaume Martinet
 P2: Tu 7:30  8:20 pm, EQuad 225; Pierre Yves Gaudreau Lamarre
 P3: M 3:30  4:20 pm, EQuad 225; Daniel Gitelman
 P4: Tu 3:30  4:20 pm, Julis Romo Rabinowitz Building A97; Kaizheng Wang
Grading and course policies
Grading: There will be homework problem sets throughout the semester (approximately weekly), as well as two midterms and a final exam.
Your final score is a combination of your performance in these, with the following breakdown:
 HW 20%
 first midterm 20%
 second midterm 20%
 final 40%
Midterm #2 info: Wednesday, May 2, in class
Final info: 7:30 pm, Monday, 21 May, 2018; location: McCosh Hall 46
Homework and collaboration policy:
Please be considerate of the grader and write solutions neatly. Unreadable solutions will not be graded.
Please write each problem on a separate sheet and turn it in to the appropriate dropbox in 123 Sherrerd Hall.
Please write your name, Princeton email, and the names of other students you discussed with on the first page of your HW.
No late homework will be accepted. Your lowest homework score will be dropped.
You should first attempt to solve homework problems on your own.
You are encouraged to discuss any remaining difficulties in study groups of two to four people.
However, you must write up the solutions on your own and you must never read or copy the solutions of other students.
Similarly, you may use books or online resources to help solve homework problems, but you must always credit all such sources in your writeup, and you must never copy material verbatim.
Advice: do the homeworks! While homework is not a major part of the grade, the best way to understand the material is to solve many problems. In particular, the homeworks are designed to help you learn the material along the way.
Email policy: For questions about the material, please come to office hours.
For general interest questions, please post to the course Piazza page.
This facilitates quick and efficient communication with the class.
Please use email only for emergencies and administrative or personal matters.
Please include "ORF 309" in the subject line of any email about the course.
Resources
Main resource (required text):
 Ramon van Handel, Probability and Random Processes (ORF 309 / MAT 380 Lecture Notes), 2016. (pdf on BlackBoard)
Think of this as a Q&A wiki for the course, use it for questions and discussions. For more details, see Piazza.
Schedule
Classes begin on Monday, February 5.
 Lecture 1 (Feb 5): Introduction and overview; van Handel Ch. 0.
 Lecture 2 (Feb 7): Basic principles of probability: sample space, events, probability measure; van Handel 1.11.3

Lecture 3 (Feb 9): Basic principles of probability: probability measure, probabilistic modeling; van Handel 1.3, 1.4
Homework 1 out, due 5 pm, Friday, February 16  Lecture 4 (Feb 12): Basic principles of probability: probabilistic modeling, conditional probability; van Handel 1.4, 1.5
 Lecture 5 (Feb 14): Basic principles of probability: conditional probability, independent events, random variables; van Handel 1.51.7

Lecture 6 (Feb 16): Basic principles of probability: random variables, expectation; van Handel 1.7, 1.8
Homework 2 out, due 5 pm, Friday, February 23  Lecture 7 (Feb 19): Basic principles of probability: expectation, distributions, and independence; van Handel 1.8, 1.9
 Lecture 8 (Feb 21): Basic principles of probability: conditional distributions and expectation; van Handel 1.8, 1.9

Lecture 9 (Feb 23): Bernoulli processes, binomial distribution, geometric distribution; van Handel 2.1, 2.2
Homework 3 out, due 5 pm, Friday, March 2  Lecture 10 (Feb 26): Bernoulli processes, arrival times, geometric distribution, law of large numbers; van Handel 2.2, 2.3
 Lecture 11 (Feb 28): Law of large numbers, variance; van Handel 2.3

Lecture 12 (Mar 2): Variance, continuous time arrivals; van Handel 2.3, 2.4
Homework 4 out, due 5 pm, Friday, March 9  Lecture 13 (Mar 5): Continuous arrival times, continuous random variables, expectation; van Handel 2.4, 3.1
 Lecture 14 (Mar 7): Expectation, CDF, density, joint density; van Handel 3.1, 3.2

Lecture 15 (Mar 9): joint, marginal, and conditional densities; van Handel 3.2
Homework 5 out, due 5 pm, Friday, March 16  Lecture 16 (Mar 12): Independence, lifetimes; van Handel 3.3, 4.1
 Lecture 17 (Mar 14): Midterm 1
 Lecture 18 (Mar 16): Lifetimes, minima and maxima; van Handel 4.1, 4.2
 Lecture 19 (Mar 26): Counting processes, Poisson processes, superposition; van Handel 5.1, 5.2
 Lecture 20 (Mar 28): Poisson processes: superposition and thinning; van Handel 5.2

Lecture 21 (Mar 30): Superposition and thinning, nonhomogeneous Poisson processes; van Handel 5.2, 5.3
Homework 6 out, due 5 pm, Friday, April 6  Lecture 22 (Apr 2): Nonhomogeneous Poisson processes, random walks, hitting times; van Handel 5.3, 6.1, 6.2
 Lecture 23 (Apr 4): Random walks, hitting times; van Handel 6.2

Lecture 24 (Apr 6): Random walks, hitting times, gambler's ruin; van Handel 6.2, 6.3
Homework 7 out, due 5 pm, Friday, April 13  Lecture 25 (Apr 9): Biased random walk, hitting times; van Handel 6.4
 Lecture 26 (Apr 11): Biased random walk, gambler's ruin, Brownian motion; van Handel 6.4, 7.1

Lecture 27 (Apr 13): Brownian motion, Gaussian distribution; van Handel 7.2
Homework 8 out, due 5 pm, Friday, April 20  Lecture 28 (Apr 16): Brownian motion, characterization, central limit theorem; van Handel 7.2, 7.3
 Lecture 29 (Apr 18): Central limit theorem, moment generating functions; van Handel 7.3

Lecture 30 (Apr 20): CLT, jointly Gaussian random variables; van Handel 7.3, 7.4
Homework 9 out, due 5 pm, Friday, April 27  Lecture 31 (Apr 23): Jointly Gaussian random variables, branching processes; van Handel 7.4, 8.1
 Lecture 32 (Apr 25): Branching processes, probability of extinction; van Handel 8.1, 8.2

Lecture 33 (Apr 27): Markov chains, transition probabilities; van Handel 9.1
Homework 10 out, due 5 pm, Wednesday, May 9  Lecture 34 (Apr 30): Markov chains, classification of states, steadystate behavior; van Handel 9.29.4
 Lecture 35 (May 2): Midterm 2
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