STAT213-23S2 (C) Semester Two 2023

Statistical Inference

15 points

Start Date: Monday, 17 July 2023
End Date: Sunday, 12 November 2023
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 30 July 2023
  • Without academic penalty (including no fee refund): Sunday, 1 October 2023


This course provides the theoretical foundations for statistical estimation and testing at an introductory level. These are essential for more advanced studies in statistics at higher levels because they facilitate a deeper understanding of statistical techniques and their applications.

To illuminate key ideas in estimation and testing, the course will focus mainly on inference for independent and identically distributed univariate data.

Topics that are usually covered include:
• Fundamentals of probabilistic modelling: Probabilities, distribution functions, densities, expectations, quantiles
• Expected values, Moment-generating functions
• Likelihood function, Maximum likelihood principle, Score function, Fisher Information
• Sufficient statistics
• Estimation: Method of Moments, Maximum likelihood estimation
• Properties of estimators: Unbiasedness, Efficiency, Consistency
• Sampling distributions, the Law of large numbers, Central limit theorem
• Interval estimation

Learning Outcomes

  • On completion of the course, you will be able to:
  • Apply various discrete and continuous univariate probability distributions in modelling statistical processes.
  • Understand the concept of sampling distributions and how to apply them.
  • Estimate unknown parameters of a given probability distribution using standard estimation techniques.


(1) one of MATH102, MATH199 or EMTH118; and (2) one of STAT101, DATA101, STAT211, EMTH119, or



Course Coordinator

Marco Reale


John Holmes


Assessment Due Date Percentage 
Assignments 10%
Test 30%
Exam 60%

To obtain a clear pass in this course, you must both pass the course as a whole (≥ 50%) and also obtain at least 40% in the final examination.

Textbooks / Resources

Course materials will be provided and no textbook is needed. After enrolling in the course, you will be able to access materials from the course web page in Learn at:

Indicative Fees

Domestic fee $824.00

International fee $4,750.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

All STAT213 Occurrences

  • STAT213-23S2 (C) Semester Two 2023