COURSE NUMBER AND TITLE: MATH 4251 Probability and Statistics I

CREDIT HOURS: 3

CATALOG DESCRIPTION: A study of combinatorics, probability, mathematical expectation, study of discrete and continuous distributions, bivariate and multivariate distributions, and moment generating functions, the central limit theorem, sampling distributions, estimation and hypothesis testing.

PREREQUISITE(S): MATH 2012 (grade of C or better)

SUGGESTED TEXT(S): Probability and Statistics, by Degroot and Schervish, Third Edition, Addison Wesley, 2002.

COURSE OUTLINE:

• Introduction to Probability – Set theory, basic probability rules, combinatorial methods, multinomial coefficients.
• Conditional Probability – independent events, Bayes theorem.
• Random Variables and Distributions – discrete and continuous distributions of a random variable, Distribution functions, Marginal and conditional distributions, Bivariate and Multivariate distributions, functions of two or more random variables.
• Expectation – mean, median, variance, moments, covariance and correlation, conditional expectation.
• Special Discrete Distributions - Bernouli, Binomial, Poisson, Hypergeometric, Geometric, Negative Binomial, Multinomial and Multivriate hypergeometric distributions.
• Special Continuous Distributions - Uniform, Exponential, Normal, Lognormal, Normal Approximation to Binomial, Gamma and Beta distribution, Bivariate distribution.