**Prerequisites & Bulletin Description**

## Course Objectives

Probability spaces, elementary combinatorics, random variables, independence, expected values, moment generating functions, selected probability distributions, limit theorems and applications. Student should have a thorough understanding of:

- Axioms of Probability
- Conditional Probability
- Independence
- Combinatorics
- Random Variables, Probability Density Functions, Cumulative Distribution Functions
- Multivariate Distributions
- Limit Theorems

## Evaluation of Students

Instructors' assessment is usually based on homework, quizzes, computer assignments, in-class exams and in-class final.

## Course Outline

- Introduction to Probability
- Definition of probability space; Axiomatic development, derivation of laws of probability, conditional probability, independence, Bayes's Theorem (3 weeks)
- Random Variables; discrete and continuous random variables, discreteand continuous probability densities,cumulative distribution function (2 weeks)
- Some Special Distributions; Discrete Uniform, Bernoulli, Binomial, Hypergeometric, Geometric, Negative Binomial, Poisson, Multinomial,Uniform, Normal, Gamma, Exponential (3 weeks)
- Mathematics Expectation; Expected value and its properties, variance and its properties, moment generating function and its properties (2 weeks)
- Multivariate Distributions; Joint densities, marginal densities, transformation of random variables, order statistics, conditional distributions, independence of random variables, conditional expectation (2 weeks)
- Limit Theorems; Chebychev's Inequality, Law of Large Numbers, Central Limit theorem (2 weeks)

## Textbooks & Software

Larson and Marx *Mathematical Statistics and Its Applications*, Prentice Hall

Hogg and Tanis, *Probability and Statistics Inference*, Prentice Hall.

Date: July, 2003