The course is on Canvas
Homework
Homework #1
Homework #2
Homework #3
Homework #4
Homework #5
Syllabus
Time and Location
M-W-FÂ Period 7 (1:55 PM – 2:45 PM)
Mondays-Wednesdays: IN CLASS (LIT 219) AND ONLINE
Fridays: 100 % ONLINE (Fridays lectures are held online for all students, including students enrolled in face-to-face learning)
Zoom link available in Canvas
Classes will be live and recorded. Recording will be available for viewing in Canvas.
Office Hours
By appointment
Textbook
There is no required text, but the following textbook is suggested:
- Sheldon M. Ross, Introduction to Probability Models, 11th Edition.
[The course will cover Chapters 1, 2, 3, 4, 5, 10, and 11]
Final Exam Date
Thursday, April 29 (4/29/2021) at 10:00 AM — 12:00 PM
Scope of the course
The course is an introduction to probability theory and stochastic processes. Many realistic models of real-world phenomena must take into account the possibility of randomness. Students will learn the language of probability and will gain experience in solving problems from pure and applied sciences using probabilistic arguments. Although the course provides mathematical background and an abstract framework is presented, the course will not discuss measure theory.
The course helps in the pursuit of careers in statistics, engineering, and computer science, and is strongly recommended for students who want to pursue graduate studies in mathematics, especially in the field of probability theory.
Prerequisite
STA 4321 — Introduction to Probability, or equivalent
Topics Covered
Topics include: Probability Space, Discrete and Continuous Random Variables, Conditional Probability, Independence, Markov chains, Poisson Process, Brownian Motion, Gaussian Process, and Simulation.
Weekly Schedule
W1: Language of probability, Sample space, Events, Random variables, Expectation
W2: Conditional probability, Bayes’ formula, Independence, Application: the Monty Hall paradox
W3: Markov chains, Transition function and transition matrix
W4: Chapman-Kolmogorov equations, Markov property
W5: First passage time
W6: Classification of states
W7: Invariant measures
W8: Application: Random walk on Z
W9: Borel-Cantelli Lemmas, Application: the monkey typewriter paradox
W10: Poisson process, Counting process
W11: Inter-arrivals and waiting times, Application: the bus waiting paradox
W12: Brownian motion, Hitting times
W13: Gaussian process
W14: Simulation
Process for Exams:
You will have 30 minutes to complete the exam (the exam will be posted on Canvas). Then, you will need to scan or take a picture of your test, and send it to me via Canvas (pdf or jpg file only).
The deadline to submit your test is xxx on xxx. Canvas will stamp your submission.
Notes and electronic devices are not allowed (Closed-book exam).