Math 451/Stat 451 (Theory of Probability)

Office Hours Monday 9:30-11:00am, Thursday 1:00-3:00pm; or by email appoitment

Lecture time MWF 8:30-9:20 am; ED 401

Textbook A First Course in Probability, by Sheldon Ross, 8th edition

Homework (30%) Homework assignments are the most important part of this course. Homework will be assigned during the semester on weekly basis. Selected homework problems will be graded. Homework is due at the beginning of the class on the dates specified on the tentative schedule. Each student will be given an opportunity to hand in an assignment late for up to two days, or two assignments late up to one day.

Midterm Exams (20% X 2) Two midterm examinations are scheduled on the days specified on the tentative schedule. A make-up examination is possible only if you get my permission before the examination, or with a doctor’s note.

Final Exam (30%) Final examination is scheduled on Thursday, December 19, 2013, from 7:30 am—9:30 am. No make-up finals.

Grading Course grades are determined by: A (90.0%-100%); B (80.0%-89.9%); C (70.0%-79.9%); D (60.0%-69.9%); F (<60.0%).

Tentative Schedule
8/26-8/30 Introduction; Basic Principle
9/2-9/6 Labor Day; no class
Multinomial Coefficients
Sample Spaces and Events, Homework 1 due. Solution due
9/9-9/13 Axioms of Probability
Some Simple Propositions
Probability and Equal Likelihood, Homework 2 due. Solution
9/16-9/20 Probability as a Set Function
Chapter Review
Conditional Probabilities, Homework 3 due Solution and Lecture notes
9/23-9/27 Bayes' Formula
Independent Events
Random Variables, Homework 4 due
9/30-10/4 Discrete Random Variables
Expected Value
Review. Sample Exam 1 with Solution
10/7-10/11 Exam 1(Chapters 1-3
Expectations of Discrete Random Variables Homework 5 due on Wednesday Oct 9.
10/14-10/18 Bernoulli Random Variables
Binomial Random Variables
Binomial Distribution Functions, Homework 6 due
10/21-10/25 Poisson Random Variables
Other Discrete Random Variables
Expected Value of Sum of Random Variables, Homework 7 due
10/28-11/1 Continuous Random Variable
Expectation and Variance of Continuous Random Variables
Uniform Random Variables, Homework 8 due

11/4-11/8 Normal Random Variables
Exponential Random Variables
Other Continuous Random Variables,
11/11-11/15 Review; Homework 9 due
Exam 2 (Chapter 4-5) Solutions to Sample Exam and selected HW problems
Joint Distribution Functions
11/18-11/22 Sum of Independent Random Variables
Expectation of Sums
Covariance, Homework 10 due
11/25-11/29 Thanksgiving Break
Thanksgiving Break
Thanksgiving Break
12/2-12/6 Conditional Expectation
Moment Generating Functions
Weak Law of Large Numbers, Homework 11 due
12/9-12/13 Central Limit Theorem
Strong Law of Large Numbers
Final Review
Solutions to Sample Final
Final Exam on Thursday
at 7:30-9:30am

Learning Outcomes
• The student will learn basic skills to calculate probabilities of random events
• The student will learn standard methods to compute expectation and variances of commonly used discrete and continuous randomly variables
• The student will attain a basic understanding of limit theorems, include the law of large numbers and the central limit theorem