702—Introduction to Statistical Theory I. (3) (Prereq: MATH 241) Fundamental theory of statistics and how it applies to industrial problems. Topics include probability, random variables and vectors and their distributions, sampling theory, point and interval estimators, and application to the theory of reliability, regression, process control and quality issues. Not to be used for M.S. or Ph.D. credit in statistics.
Sample Course Homepage: Recent Semester
Usually Offered: Odd Numbered Falls
Purpose: To expose the student to the basic concepts of theoretical statistics necessary for the solid understanding of the statistical procedures and methods typically used by practicing industrial personnel at an advanced level.
Current Textbook: Mathematical Statistics and Data Analysis (2nd edition), by John A. Rice, Duxbury Press, 1995.
|Introduction to Probability: sample spaces, events, counting methods, axioms, laws of probability, conditional probability, independence, Bayes' rule||
|Random Variables and Distributions I - Discrete Distributions: densities, distributions, expectation, generating functions, various discrete distributions||
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|Random Variables and Distributions II - Continuous Distributions: densities, distributions, expectations, moment generating functions; gamma, normal, Weibull distributions and applications to life testing and quality control, in particular; Chebyshev's inequality, normal approximations, transformation of variables||
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|Random Variables and Distributions III - Joint Distributions: discrete and continuous cases; covariance, correlation and independence; conditional distributions and expectations with applications||
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|Sampling Distributions: central limit theorem; chi-square, t, and F distributions; distribution of sample mean and sample variance||
|Sampling and Estimation: random sampling and statistics, likelihood, maximum likelihood estimation, method of moments estimation, Bayes methods, interval estimation||
The above textbook and course outline should correspond to the most recent offering of the course by the Statistics Department. Please check the current course homepage or with the instructor for the course regulations, expectations, and operating procedures.