The
University of Massachusetts Boston
Department
of Mathematics
MA345
Probability I, Spring 2025
Instructor: Prof. Alfred Noël
Office: 3-154-14 Wheatley
Phone: (617)-287-6458
Email: alfred.noel@umb.edu
URL: http://www.math.umb.edu/~anoel
Class hours: MW5:30 PM - 6:45 PM
Room W-2-127
Office hours: MW: 1:00 PM – 3:00 PM
Text :
Introduction to Mathematical Statistics and its applications 5th
edition by Larsen and Marx Publisher Pearson 9780321693945
NO COMPUTERS NO CELL PHONES
IN CLASS
Course Info: This is an introductory Calculus based course in Probability
Theory, one of the most fundamental tools in Mathematics and Science. The
students are expected to be mathematically mature enough to start dealing with
concepts beyond Calculus ||. The goal of this course is to give to students a
set of mathematical tools that they will need in order to pursue advanced
studies in Mathematics, Physics, Chemistry, Engineering in particular and
Science in general. Students who are concerned about their mathematical
background should speak to me as soon as possible for advising. Students who
have taken Calculus I, II, should, in principle, be able to take this course.
However, regardless of your background you will find the course to be very
challenging. Consequently, you should not collaborate on homework and you
should participate in class discussions. Also, I strongly advise students to
form discussions groups that meet outside of the class-room. We will cover the
first four chapters of the texts: Discrete and Continuous Random variables,
Joint Distributions, Moment generating functions, Central Limit Theorem. Here
are the topics:
1. Introduction
1.1
An Overview
1.2
Some Examples
1.3 A
Brief History
1.4 A
Chapter Summary
2. Probability
2.1
Introduction
2.2 Sample
Spaces and the Algebra of Sets
2.3
The Probability Function
2.4
Conditional Probability
2.5
Independence
2.6
Combinatorics
3. Random
Variables
3.1
Introduction
3.2
Binomial and Hypergeometric Probabilities
3.3
Discrete Random Variables
3.4
Continuous Random Variables
3.5
Expected Values
3.6
The Variance
3.7
Joint Densities
3.9
Further Properties of the Mean and Variance
3.12
Moment-Generating Functions
4. Special
Distributions
4.3
The Normal Distribution, Approximations, Central Limit Theorem
Appendix
4.A.2 A Proof of the Central Limit Theorem
Exams: There will be weekly homework assignments, two 75-minute
exams, and a final exam.
Exam I : Wednesday, February 26
Exam II : Wednesday, April 9
Grading Procedures: Homework
25%, Exam1 20%, Exam2 25%, Final Exam 30%.
THERE WILL BE NO MAKEUP EXAMS.
STUDENTS ARE RESPONSIBLE FOR MATERIAL COVERED IN CLASS.
