Instructor: Xia Chen
Office: Ayres 318, (Phone: 974-4284).
Email: xchen3@tennessee.edu
Website: http://www.math.utk.edu/~xchen
Class: MWF 1:50 pm. -2:40 pm. (HBB 121)
Office Hours: MWF 10:00 am.- 11:00 am.
Text Book: Probability: A graduate course, 2nd edition (by Allan Gut).
Course Description:
This is the first half of a year-long graduate course series (the second
half is Math 524 in the Spring 2023) in probability. In this semester,
we will provide
a rigorous treatment of the materials such as
probability space, random variable (expectation, independence, etc.),
convergence theorems, zero-one laws, Borel-Canttelli lemma and distribution
theory. In the Spring of 2023, we will continue on
the same book with more advanced and special topics such as
inequalities in probability,
characteristic functions, convergences of random variables
law of large numbers, Central limit theorem
and martingales.
I will give planty of examples to help understanding a variety of
concepts introduced during the course.
I plan to keep this course self contained, and will not assume material
other than what is covered in the first course of
probability and in advanced calculus.
In particular, I will not assume results from
measure theory, which will be developed as part of the course.
Tests:
Grading: Final Exam 30%; Midterm 20%; Homework 50%
Letters will be assigned as follows (subject to change): A:90-100%, B:80-89%, C:70-79%, D:60-70%, F:59% or below.
Homework #1
Chapter 1: Exercise 2.2, Exercise 2.6,
Problems in 1.6: 4, 5, 11, 12, 13.
Solution to Homework #1 (pdf)
Homework #2
Chapter 2: Exercise 1.3, Exercise 3.1;
Problems in 2.20: 1, 2, 3, 4, 5, 8
Solution to Homework #2 (pdf)
Midterm test solution (pdf)
Homework #3
Chapter 2: Exercise 5.1, Exercise 5.2, Exercise 10.4,
Exercise 11.2, Exercise 12.3(a).
Problems in 2.20: 13, 15, 16, 18, 19, 20.
Solution to Homework #3 (pdf)
Homework #4
Chapter 3: Problems in 3.10: 2, 3, 5, 6, 7(a), 8.
Chapter 5: Problems in 5.14: 1, 5, 11.
Solution to Homework #4 (pdf)
Final exam solution (pdf)