# Math 155H: Introduction to Probability

## Winter 2008

 Instructor: To be announced
 Secretary: Carolyn Johns Email: math@trentu.ca or cjohns@trentu.ca Office Phone: 748-1011 x7531 Fax: 748-1155 Office: Peter Gzowski College 342

### COURSE  TOPICS

Mathematics 155H is an introduction to probability for students with a background in calculus covering topics as listed in the outline below. (It is not a course in statistics.)

### TEXT

Fundamentals of Probability, by Saeed Ghahramani (Pearson, 3rd edition). (A copy is on reserve in the library.)

### PREREQUISITES

This course is intended for students who have completed an introductory course in calculus.  The mathematics prerequisite is Mathematics 105H (or Mathematics 110 as a co-requisite) or equivalent. A list with the minimal Calculus concepts and operations that students are assumed to be comfortable with can be found in the appropriate link on WebCT.

### COURSE OUTLINE

1. Introduction
1. Axioms of Probability
2. Counting Techniques
3. Conditional Probability and Independence
2. Discrete Random Variables
1. Random Variables
2. Expected Value and Variance of a Discrete Random Variable
3. Specific Discrete Random Variables
1. Binomial Random Variables
2. Poisson Random Variables
3. Geometric and Negative Binomial Random Variables
4. Hypergeometric Random Variables
3. Continuous Random Variables
1. Density and distribution functions
2. Expectations and Variances
3. Uniform Distribution
4. Exponential Distribution
5. Normal Distribution
6. The Gamma and the Chi-Squared Distributions
7. Distribution of Functions of Random Variables
4. Sums of Independent Random Variables and Limit Theorems
1. Moment Generating Functions
2. Laws of Large Numbers
3. The Central Limit Theorem
5. Joint distributions

### COURSE EVALUATION

The course is evaluated through problem sets, midterm examinations, quizzes and a final exam. The exact weights for each will be announced by the instructor on the first day of classes.

### WORKSHOPS

There will be optional workshops during the semester. These workshops will be used for discussion of homework assignments, practice problems and general questions. Each student can attend any workshop he/she desires (please refer to the schedule in the academic timetable). If there were problems with the classroom size, then each student will be asked to attend only the workshop he/she has signed up for. Please check the schedule every week to make sure that you attend only on the right dates.

### CALCULATOR

Due to the amount of numerical work involved in this course, students should have a scientific calculator, and should bring it to every class.  A graphing calculator is not required, but it is allowed.

### PLAGIARISM

By order of the Senate, the following notice appears on this syllabus:

Plagiarism is an extremely serious academic offence and carries penalties varying from failure in an assignment to suspension from the University. Definitions, procedures, and penalties for dealing with plagiarism are set out in Trent University's Academic Dishonesty Policy, which is printed in the 2007-2008 Academic Calendar.