Math 451 syllabus
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: MA 227 Minimum Grade of C and MA 237 Minimum Grade of C
Suggested Text: Mathematical Statistics with Applications, 7th edition by Dennis D Wackerly, William Mendenhall, Richard L Scheaffer. Published by Duxbury Press.
Coverage: Chapter 1 (all sections) , Chapter 2 (all sections), Chapter 3 (omit 3.10), Chapter 4 (omit 4.11), Chapter 5 (omit 5.10), Chapter 6 (omit 6.6), Chapter 7 (all sections)
Learning outcomes: Upon the successful completion of the course a student will:
- Understand set algebra, events, probability and laws of probability.
- Know conditional probability, law of total probability, Bayes' rule, independence of events and random variables.
- Know discrete random variables including probability distribution, expected value, the binomial, geometric, negative binomial, hypergeometric, and Poisson distributions, moment generating functions and Tchebysheff's theorem.
- Understand continuous random variables including the density function, cumulative distribution function, expected value, the uniform, normal, gamma, beta, exponential, and chi-square distributions, moments, and Tchebysheff's theorem.
- Understand multivariate probability distributions, including the multivariate, marginal, and conditional distributions, independent random variables, the expected value a function of random variables, and covariances.
- Understand functions of random variables, including finding the probability distribution of a function of random variable, the Cdf method, the method of transformation, and the mgf method.
- Understand sampling distributions related to the normal distribution, the central limit theorem, and the normal approximation to the binomial distribution.