Math 155F-A: Introduction to Probability

Fall 2003

Instructor:Ion Rada Email:

ion@euclid.trentu.caOffice Phone:748-1011 x5264 Office hours:Tuesday 2-3pm, Wednesday 3-4 pm, Thursday 12-1pm Office:Champlain College J12

Secretary:Carolyn Johns Email:math@trentu.caor cjohns@trentu.caOffice Phone:748-1011 x1531 Fax:748-1630 Office:Lady Eaton College N126

COURSE TOPICSMathematics 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, but statistical applications will be covered if time permits.

TEXTProbability: an Introduction with Statistical Applications,by John J. Kinney (Wiley, 1997).

COURSE OUTLINE

- Introduction

- Axioms of Probability
- Conditional Probability and Independence
- Counting Techniques
- Discrete Random Variables

- Random Variables
- Expected Value and Variance of a Discrete Random Variable
- Specific Discrete Random Variables

- Bimomial Random Variables
- Geometric and Negative Binomial Random Variables
- Hypergeometric Random Variables
- Poisson Random Variables
- Continuous Random Variables

- Density and distribution functions
- Uniform Distribution
- Exponential Distribution
- Normal Distribution
- The Gamma and the Chi-Squared Distributions
- Functions of Random Variables

- Distribution of Functions of Random Variables
- Moment Generating Functions
- The Central Limit Theorem
- Multivariate distributions

STUDENT BACKGROUND

Mathematics: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 corequisite) or equivalent. A short description of the the calculus requirements can be found here.

Computing:Previous specific computing experience is not required for the course.

Calculators:Due to the amount of numerical work involved in this course, students should possess a calculator. If time permits, there will be some discussion of statistical applications; thus, a calculator with built-in statistical function keys will be useful.

LECTURES

Wednesday 11:00 - 11:50 am ECC 201 Thursday 3:00 - 3:50 pm SC 137 Friday 9:00 - 9:50 am ECC 201 Lecture hours will be used for the presentation of course material and for general discussion and questions related to the course material including problem sets. Students are responsible for all material covered in lectures and for all announcements made in lecture hours. Students who miss classes, thus, must ensure that they determine what material was covered and what announcements were made in the missed classes.

WORKSHOPS (fortnightly)

Tuesday 1:00 - 1:50 pm ESC B319 Thursday 1:00 - 1:50 pm SC 115 Friday 12:00 - 12:50 ESC B319 ## ASSIGNMENTS

Assignment problem solutions are to be submitted in class on the day they are due. No late submissions are accepted unless they are arranged in advance.

Assignment #2

Assignment #3: presentation of Negative Binomial or Hypergeometric Distribution (pmf, cdf, expectation - proof, variance - proof, applications)## FINAL EXAMINATION

There will be a final examination on 8 December, 2003 - 8 AM - OCA 208. Practice by looking at these exam samples:

## MIDTERM EXAMINATION DATE

There will be a midterm examination on Friday, October 31. Practice for the midterm by looking at the midterm exam samples above. Also, take a look at the following problems from our textbook: ex/page 10/9, 8/16, 6/30, 29/31, 22/64, 24/64, 3/87, 1/97, 13/98, 11/107, 22/108, 7/134, 13/168, 18/168, 20/168, 21/168.

COURSE EVALUATION

Assignments (five):Each assignment will contribute 9% of the final mark.

Midterm examination:The midterm exam will contribute 25% of the final mark.

Final Examination:There will be a final three-hour examination. The final examination will contribute 30% of the final mark.

Summary:

Problem sets: 5 x 9% 45% Midterm exam 1 x 25% 25% Final exam 1 x 30% 30% 100% ## 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 2003-2004 Calendar Supplement.