Rutgers-The State University of Rutgers
Introduction to Probability (26:960:575 Sec (02) )
Fall 2012
Wednesday 9:00-12:50
1 Washington Park, Room 204
Instructor: Professor J. Tavantzis (tavantzi@rutgers.edu)
Office: 1072 Washington Park
Phone: 973-601-3970
Office Hours: by appointment
Course Objective:
This course is an introduction to probability combining both applications and theory. The course is a
prerequisite for stochastic processes and in particular for Stochastic Calculus for Finance to be given
Spring 2013.
Syllabus:
Text: Probability Theory and Random Processes by Geoffrey Grimmett and David Stirzaker, ISBN 978 19
857222 0
Reference: Probability an Introduction by Geoffrey and Welsh, ISBN 978 0 19 853264 4
Week
1. Events, sigma-fields, probability and conditional probability
2. Independence, product spaces and problems
3. Random variables, discrete and continuous, law of averages
4. Random vectors, Monte Carlo simulation and problems
5. Discrete random variables, mass functions, expectation, examples of discrete random variables
6. Conditional distribution and expectation, sums of random variable, simple random walk
7. Continuous random variables, examples of random variables, conditional distributions and
expectations
8. Multivariate distribution, geometric probabilities and problems
9. Generating functions and applications, random walk continued
10. Characteristic functions with examples, problems
11. Markov chains, classification of states and chains, stationary distribution
11. Limit theorem, reversibility, chains with finitely states
12. Modes of convergence, law of large numbers, strong laws
13. Martingales, filtrations, Wiener Process
14. Martingales( continued)
15. Final Exam
Grading:
Assignments
33 1/3%
Quizzes
33 1/3%
Final
33 1/3%
Honor Pledge
Rutgers University, in conjunction with the RBS Committee comprised of faculty, students and staff, has
established an Honor Code that states:
“I pledge on my honor, that I have neither received nor given any unauthorized assistance on this
examination.”