Instructor
Dr. William J. Thistleton
Associate Professor of Mathematics
Donovan 2269
315-792-7508
thistlet@sunyit.edu

Find us on the Web
http://www.math.sunyit.edu/math/mat370

Class Meetings
Classes meet on Tuesday and Thursday afternoons in Donovan G244 from 4:00 PM - 5:50 PM. Note: Check the Snow Line at 792-7385 or www.sunyit.edu at Quick Links: Cancelled Classes during inclement weather.

Office Hours
Formal office hours will be on Tuesdays and Thursdays from 2:00 till 4:00 PM.

Prerequisites
Calculus II, MAT322 or equivalent. Note that good integration skills and a facility with summation notation are necessary for success in this course.

Catalog Course Description
This course is an introduction to the theory of probability and its applications. Topics covered include: basic set theory, elementary probability, counting arguments, conditional probability and independence, random variables and their properties, functions of random variables, distribution functions, probability models and applications such as stochastic processes.

Required Text
Probability for Risk Management, 2nd Edition by Matthew J. Hassett and Donald G. Stewart, Actex, ISBN-10: 1566985833, ISBN-13: 9781566985833 (2006).

Strongly Reccomended Text
Student Solutions Manual for Probability for Risk Management by Matthew J. Hassett and Donald G. Stewart, Actex.

Required Computational Environment

MATLAB

Attendance
Your presence in class is needed on a daily basis. The material presented in this course continually builds upon past lectures. Please don't fall behind!

Course Outline

• Introduction to Desriptive Statistics: Graphical Procedures, Measures of Central Tendency, and Measures of Dispersion.
• Definition of Probability and Basic Rules
• Set Theory and the Sample Space
• Methods of Enumeration (Counting)
• Conditional Probability and Independence
• Discrete Random Variables: Probability Mass Functions and Cumulative Distribution Functions
  • Bernoulli, Binomial, Geometric, Poisson, Hypergeometric, etc.
• Continuous Random Variables: Probability Density Functions and Cumulative Distribution Functions
  • Uniform, Exponential, Gamma, Normal, Beta, Weibull, t, F, chi2, etc.
• Functions of Random Variables
• Expectation and Variance for Random Variables and Functions of Random Variables
• Bivariate and Marginal Probability Distributions
• Conditional Probability Distributions
• Conditional Expectations
• Covariance and Correlation
• Sums of Random Variables and Sampling Distributions
• Central Limit Theorem
• Confidence Intervals (Z,t)
• Hypothesis Testing of SIngle and Multiple Samples, P-Values, Paired Data
• Tchebysheff's Theorem
• Moment Generating Functions
• Entropy
• Applications and Probability Models
• Computer Applications (MATLAB).

Texts for further reading

• An Introduction to Probability Theory and Its Applications by William Feller, Wiley (1968).
• Introductory Probability and Statistical Applications by Paul L. Meyer, Addison-Wesley (1970).
• Introduction to Probability Models, 5th Edition, by Sheldon M. Ross, Academic Press (1993).
• Introduction to Stochastic Processes by Paul Hoel, et al. Houghton Mifflin (1972).
• Probability and Measure by Patrick Billingsley, John Wiley and Sons, (1995).
• Introductory Applied Probability, by G.P. Beaumont, Ellis Horwood Limited, (1983).
• Probability, Modeling Uncertainty, by Barr and Zehna, Addison- Wesley, (1983).
• Probability and Stochastic Processes, by Leo Breiman, Houghton Mifflin, (1969).
• Applied Probability, by W.A. Thompson, Jr., Holt, Rinehart, and Winston, (1969).

Methods of Evaluation
There will be two exams and a final. The first exam will be on Thursday February 26 (Lecture 12). The second exam will be on Thursday April 9 (Lecture 22). There will also be weekly homework assignments and a project. The breakdown for these is as follows:

• 25% for each exam
• 30% for final
• 10% for project
• 10% for homework