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Mathematical Statistics I


Course Description

Concepts and basic properties of some special probability distributions, independence, moment generating functions, sampling distributions of statistics, limiting distributions.


Athena Title

Mathematical Statistics I


Prerequisite

MATH 2270 or MATH 2500


Semester Course Offered

Offered fall


Grading System

A - F (Traditional)


Student Learning Outcomes

  • Students will learn how to use specific statistical distributions and general modes of statistical thinking to make inferences from data, and to support an argument with quantitative information.
  • Students will learn the mathematical and probabilistic underpinnings of statistical theory, which is essential for understanding and properly applying statistical techniques used in other fields such as economics, biology, engineering, social science, and so on.
  • Students will apply a wide variety of probability distributions, and approach and solve practical problems through statistical and probabilistic reasoning.
  • Students will be able to prove theorems relating to the content of the course, provide written explanations of the ideas behind statistical concepts, and will have improved their skills at solving complex and multi-step problems.

Topical Outline

  • Set operations
  • laws of probability
  • conditional probability and Bayes' theorem
  • discrete distributions
  • continuous distributions
  • bivariate and multivariate distributions
  • distributions of functions of random variables
  • sampling distributions
  • moment generating functions
  • laws of large numbers and central limit theorems

Syllabus