Course: B90.3301.01/C22.0014.001 - Introduction to the Theory of Probability Semester: Spring 2002 Class Hours: Thursday 6:00 - 8:50 PM Class Room:  KMEC Instructor: Professor Aaron Tenenbein Office: K-MEC 8-58  Tel: (212) 998-0474 Office Hours: Thursday 3 - 6 PM; other times by appointment Email: atenenbe@stern.nyu.edu

Course Outline

Courses offered by the Department of Statistics and Operations Research can be broadly categorized as methodological with emphasis on applications, and theoretical. The course, Introduction to the Theory of Probability is primarily a theory course. However, applications to various topics in economics, finance, marketing, and operations will be discussed in order to illustrate the theoretical aspects of probability.

This course is designed to present the major ideas of probability, probability distributions, and probability modelling. It serves as preparation for many courses including applied statistics, stochastic processes, mathematical finance, and actuarial science. In particular this course will cover the concepts needed for the probability portion of actuarial examination 1.

Course Topics

1. Probability Concepts.
2. Probability Distributions, Moment Generating Functions, Means, Variances and Measures of Skewness and Kurtosis
3. Particular Probability Distributions
1. The Binomial Distribution with Applications to Bond Default Rates and Quality Control
2. The Normal Distribution with Application to Rate of Return Distributions
3. The Poisson Distribution, with Applications to Insurance
4. The Lognormal Distribution with Application to Income Distributions and Option Pricing
5. Gamma, Chi-Square, t and F Distributions
4. Bivariate and Multivariate Distributions and Correlation Coefficients
5. Particular Bivariate Distributions, Multinomial and Multivariate Normal Distributions, with applications to Portfolio Analysis
6. Transformation of Variables and Sampling Theory, the t, and F Distributions.
7. Limit Theorems including the Central Limit Theorem.

You may select one of the two texts for the course. The homework problems will be from Hogg and Craig 5th edition and will be distributed in class.

(HC) Hogg, R. V. and Craig, A.T. (1995),"Introduction to Mathematical Statistics", fifth edition, New Jersey: Prentice Hall. This book provides a rigorous discussion of topics.

(HT) Hogg, R.V. and Tanis, E.A. (2001), Probability and Statistical Inference, sixth edition, New Jersey: Prentice Hall. A more verbal presentation of concepts.