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
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