UAH > Math > Courses > MA 452/502

MA 585, Probability

Course Description

Probability spaces

• random variables
• conditional probability
• independence
• modes of convergence
• introduction to sigma-algebras and measurability

Distributions

• discrete distributions
• continuous distributions
• joint and marginal distributions
• transformations of random variables
• distribution and quantile functions
• convergence in distribution

Expected value

• properties of general expected value
• mean, variance, and covariance
• generating functions
• conditional expected value

Special models and distributions

• Bernoulli trials and the binomial and negative binomial distributions
• the Poisson model and the Poisson, exponential, and gamma distributions
• finite sampling models and the hypergeometric distribution
• the normal distribution

Fundamental theorems

• the law of large numbers
• the central limit theorem

Prerequisites

• MA 201, Calculus C
• MA 385, Introduction to Probability and Statistics or MA 385, Introduction to mathematical statistics or ISE 390

Credit

3 Semester Hours

Grading System

This course is graded A, B, C, D, F. The grade typically depends on a combination of class tests, homework assignments, and a comprehensive final exam.

Spring 2008

• MA 585-01, Dr. Donshgeng Wu