MA371 PROBABILITY (3 Cr.)

COURSE DESCRIPTION

Prerequisite: MA211 and MA 265

Offered:  Fall

General Introduction and Goals

A general introduction to the basics of statistics, introduction to discrete and continuous probability distributions and generating functions, and derivation of distributions of functions of random variables.  Finally, sampling distributions and limit theorems.

Goal/Purpose
MA371 consists of a study of the theory of elementary probability and statistics.  Discrete and continuous probability functions are investigated, and moments and moment generating functions are developed for both univariate and multivariate functions.  Marginal and conditional distributions are found, as well as limiting distributions and distributions of functions of random variables.  Applications are discussed when they contribute to understanding the theory being developed.

Objectives
The student will:

1. become familiar with probability and statistical methodology and terminology.
2. learn how to manipulate and evaluate series summations.
3. learn how to find moments and moment generating functions, and be able to interpret moments.
4. find probabilities and understand the role of probability in statistical decision making.
5. learn how to find limiting, marginal and conditional distributions from given probability distribution.
6. learn how to find the distributions of functions of random variables given the distributions of the variables.

Course Content Outline

1. Introductory Probability
   1. Set notation and definitions
   2. Calculating probability
   3. Event composition and rules of probability
   4. Conditional probability
   5. Baye's Rule
2. Discrete Random Variables
   1. Binomial, negative binomial, hypergeometric and Poisson probability distributions
   2. Expected values
   3. Moment generating functions
   4. Probability generating functions
3. Continuous Random Variables
   1. Uniform, normal, gamma and beta distributions
   2. Expected values
   3. Moment generating functions
   4. Tchebysheff's Theorem
   5. Expected values for discontinuous and mixed distributions
4. Multivariate Probability Distributions
   1. Multivariate distributions
   2. Marginal and conditional probability distributions
   3. Independence and covariance
   4. Expected values of functions of random variables
   5. Conditional expectations
5. Functions of Random Variables
   1. Finding the probability distribution of a function of random variables
   2. Distribution function, transformation, and moment generating function methods
   3. Order statistics
6. Sample Distributions
   1. Sampling distributions related to the normal distribution (Chi-square, F and T distributions)
   2. The Central Limit Theorem
   3. Limiting distributions