UAH

Graduate Courses

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 487, 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.