Probability Theory: Math 407
Instructor: Larry Goldstein, larry@usc.edu
Course Prerequisite: USC MATH 226 or MATH 227, or an equivalent advanced multivariate calculus course.
Text and Course Coverage
Introduction to Probability, by David Anderson, Timo Seppalainen, and Benedek Valko
The course will cover the following material:
Chapter 1: Experiments with random outcomes, Sections 1.1-1.5
Chapter 2: Conditional probability and Independence, Sections 2.1-2.4
Chapter 3: Random Variables: Sections 3.1-3.5
Chapter 4: Approximations of the binomial distribution, Sections 4.1-4.6
Chapter 5: Transforms and transformations, Sections 5.1-5.2
Chapter 6: Joint distributions of random variables, Sections 6.2-6.3
Chapter 9: Tail bounds and limit theorems, Sections 9.1-9.3
Exams and Grading Policy
- 15% Attendance
- 25% Midterm exam, May 21st. Midterm Solutions
- 35% Final Exam, June 7th,
- 25% Four Quizzes, two on the first two Thursdays of the problem session, and the next two on the last two Tuesdays, covering the material since the previous quiz up to the Tuesday/Friday of the week of the quiz.
Assignments
Chapter 1: 1,2,8,9,12,13,16,19,21,23,30,32,41,43,51,58,59
Chapter 2: 2,5,9,11,14,19,21,22,31,34,48,67,85,88
Chapter 3: 1,3,7,9,15,17,31,40,46,52,56,57,58,63,66,69,74,77
Chapter 4: 3,5,11,12,15,20,23,28,32,35,36,41,44,49,50,52,53,54,56
Chapter 5: 2,5,7,9,10,16,18,20,21,22,24,28,31,33,37,39,40,43
Chapter 6: 7,13,15*,18,19,21,22,29,36,39,47,50*,55,57,58,60* (*=optional)
Chapter 7: 7.4, 7.15
Chapter 9: 2,4,17,20,21*,24*,25* (is the condition |Cov(X_i,X_{i+1})| ≤c needed?), 26 (you may add additional conditional on the behavior of E[T_n]),27*, 29*, 32*, 33* (*=optional)
Class notes: May 13: 1, 2, 3, 4, 5, 6, 7, 8
June 5 (too large for this page, uploaded to University (USC/LUISS) specific site)