## Department of Mathematics

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MATH 440: Probability and Statistics I

#### 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.

Submitted
Date: July, 2003