University of Rhode Island    Department of Mathematics

MTH 451

Intoduction to Probability and Statistics 

Spring 2018

TTh 12:30 - 1:45 p.m. 


Instructor: Dr. M. Kulenovic, Lippitt 202D, 874-4436, mkulenovic@


TextH. Pishro-Nik: Introduction to Probability, Statistics and Random Processes, Kappa Research 2016

Prerequisites: MTH 243 or equivalent

Calculators: A graphing calculator is required

Office Hours: TWTh 11-12 

Room: Lippitt 205




H. Pishro-Nik: Introduction to Probability, Statistics and Random Processes


Online version of the book:

Additional Texts:(Excellent sources of solved problems)

Grinstead and Snell, Introduction to Probability (available for free download from:


Robert Ash

Basic Probability Theory, Dover (available for free download from:


Professor A.J. Hildebrand’s collection of solved problems:



Combinatorial Methods, Probability, Random Variables, Generating Functions, Probability Distributions and Probability Densities, Mathematical Expectation, Special Probability Distributions, Functions of Random Variables, Law of Large Numbers and Central Limit Theorem.


Homework (15%), quizzes (15%), midterm exam (20 %), second exam (20 %);  a comprehensive final exam (30 %) 

About the Course

MTH 451 is an introduction to the mathematical theory of probability using calculus. Probability theory has a tremendous range of applications in all the sciences, including the social sciences, business and economics, and provides the mathematical foundation for statistics. It uses a wide variety of mathematical techniques and concepts, especially elementary set theory, combinatorics and calculus. A main goal of this course is that you will be able to read more advanced material on probability and its applications and go on to courses in mathematical statistics and stochastic processes. The class is designed for an audience with quite diverse interests such as an engineering, science, economics or business major. It is great preparation for the first actuarial exam. The probability will be a basic part of your mathematical toolkit; if you are a secondary math education major, you will most likely need to take the Praxis content exam, which contains material on discrete mathematics and probability for which this course is great preparation; if you are interested in taking the actuarial exams, this course is absolutely fundamental. Probability theory is a fundamental discipline in mathematics itself as well as the foundation for all of statistics. In addition, the study of Probability Theory can be entertaining, enlightening and sometimes surprising.

Mathematica Notebooks (developed by Professor Kulenovic and available  in
Sakai site of the course): 

Sakai There will be practice problems and solved problems in Sakai site of the course.

How to get help
I may help you with questions, just stop by my office.

Special Accommodations
Students who need special accommodations and who have documentation from Disability Services (874-2098) should make arrangements with Dr. Kulenovic as soon as possible.


The Authors of the Grinstead and Snell textbook have prepared a set of programs to go with the book. There are Mathematica, Maple versions of these programs. You can download the programs from this location. There are also experimental versions of the programs as Java applets

MTH 451Intoduction to Probability and Statistics - Spring 2018




Suggested Homework Problems 

Monday January 22

 Start of the course










Exam 1








 Exam 2