The course is on Canvas
Homework
Homework #1
Homework #2
Homework #3
Homework #4
Homework #5
Simulation of Random Variables
Syllabus
Time and Location
M-W-F Period 7 (1:55 PM – 2:45 PM) in FLI 111
Office Hours
Monday 10:30am – 11:20am, Wednesday 10:30am – 11:20am, or 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, May 4 (5/04/2023) at 3:00 PM — 5:00 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