STATS 426 - Introduction to Theoretical Statistics
Fall 2022, Section 001
Instruction Mode: Section 001 is  In Person (see other Sections below)
Subject: Statistics (STATS)
Department: LSA Statistics
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Requirements & Distribution:
Waitlist Capacity:
Enforced Prerequisites:
(MATH/STATS 425 or STATS 412) and (MATH 214 or MATH 217).
This course counts toward the 60 credits of math/science required for a Bachelor of Science degree.
May not be repeated for credit.


This course covers the basic ideas of statistical inference, including sampling distributions, estimation, confidence intervals, hypothesis testing, regression, analysis of variance, nonparametric testing, and Bayesian inference. The sequence of STATS 425/426 serves as a prerequisite for more advanced Statistics courses. Regular homework and a final exam.

Topic covered include:

  • Random Variables
  • Joint Distributions
  • Induced Distributions
  • Expectation
  • The Law of Large Numbers
  • The Central Limit Theorem
  • Simulation
  • Populations and Samples
  • The Chi-squared, t, and F Distributions
  • Estimation: The Method of Moments
  • Maximum Likelihood Estimation
  • Bias, Variance, and MSE
  • The Cramer Rao Inequality
  • Exponential Families and Sufficiency
  • Confidence Intervals
  • Approximate Confidence Intervals
  • The Bootstrap
  • Asymptotics of the MLE
  • Tests and Confidence Intervals
  • Neyman Pearson
  • Likelihood Ratio Tests
  • Chi-Squared Tests
  • Goodness of Fit Tests
  • The Sample Distribution Function
  • Decision Analysis
  • Bayesian Inference
  • The Two Sample Problem
  • More on the Two Sample Problem
  • Rank Tests
  • One Way ANOVA
  • Simultaneous Confidence
  • Two Way ANOVA
  • Categorical Data
  • Simple Linear Regression
  • Multiple Regression



STATS 426 - Introduction to Theoretical Statistics
Schedule Listing
001 (LEC)
 In Person
TuTh 2:30PM - 4:00PM
Note: The Department of Statistics must allow students who are declared in its programs the opportunity to register for Statistics classes needed to complete their programs. Any remaining seats reserved for Statistics students will be opened after registration is complete and waitlists have been evaluated.

Textbooks/Other Materials

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Syllabi are available to current LSA students. IMPORTANT: These syllabi are provided to give students a general idea about the courses, as offered by LSA departments and programs in prior academic terms. The syllabi do not necessarily reflect the assignments, sequence of course materials, and/or course expectations that the faculty and departments/programs have for these same courses in the current and/or future terms.

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