Math 451 syllabus

Probability

Course Description:
A comprehensive introduction to probability, the mathematical theory used to model uncertainty, covering the axioms of probability, random variables, expectation, classical discrete and continuous families of probability models, the law of large numbers and the central limit theorem. Credit for both MA 451 and MA 550 is not allowed.

Prerequisites:   “C” or better in MA 227 and MA 233.

Textbook:   Mathematical Statistics with Applications, 7th edition by Dennis D Wackerly, William Mendenhall, Richard L Scheaffer.  Published by Duxbury Press.

ISBN 0495110817

Coverage:

Chapter 1 - (All sections) - 0.5 weeks

Chapter 2 - (All sections) - 2.5 weeks

Chapter 3 - (omit 3.10) - 2 weeks

Chapter 4 - (omit 4.11) - 24 weeks

Chapter 5 - (omit 5.10) - 13 weeks

Chapter 6 -  (omit 6.6) - 2.5 weeks

Chapter 7 - (omit 7.4) - 1.5 weeks

Note - time allotments are approximate and do not include exams.

Learning Objectives

- Set algebra, events, probability, laws of probability. Combinatorics, calculating probabilities

- Conditional probability, law of total probability, Bayes' rule, independence of events, random variables

- Discrete random variables. Probability distribution, expected value. Distributions: binomial, geometric, negative binomial, hypergeometric, and Poisson. Moment generating functions, Tchebysheff's theorem

- Continuous random variables. Density function, cumulative distribution function, expected value. Distributions: uniform, normal, gamma, beta, exponential, and chi-square. Moments, Tchebysheff's theorem

- Multivariate probability distributions. Probability distributions: multivariate, marginal, and conditional. Independent random variables. The expected value a function of random variables. Covariances

- Functions of random variables. Finding the probability distribution of a function of random variable. Cdf method, method of transformation, mgf method.

- Sampling distributions related to the normal distribution. The central limit theorem. The normal approximation to the binomial distribution.

Last Updated February 13, 2014