MATH 440: Probability and Statistics I


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