STATS 210 : Statistical Theory


2024 Summer School (1240) (15 POINTS)

Course Prescription

Probability, discrete and continuous distributions, likelihood and estimation, hypothesis testing.

Course Overview

STATS 210 introduces the theory that underlies the statistical methods used in practical statistics courses. It is aimed at students who enjoy maths and are interested in probability and statistics. It is a core course for students in the Statistics and Probability pathway and optional for those pursuing the Applied Statistics pathway, a Statistics major, or a Data Science Specialisation. It is useful for students with interests in Econometrics, Operations Research, Finance, and theoretical aspects of Marketing Research, as well as those who have Maths or Statistics as their main interest. STATS 210 is a prerequisite for STATS 310.

If you have a weak mathematics background (C+ or lower in Stage 1 mathematics and/or STATS 125) then it is recommended that you take STATS 210 after passing the stage 2 mathematics co-requisite rather than taking it at the same time as the stage 2 mathematics co-requisite. Doing this will substantially improve your chances of passing this course.

Course Requirements

Prerequisite: 15 points from ENGSCI 111, ENGGEN 150, STATS 125 Corequisite: 15 points from MATHS 208, 250, ENGSCI 211 or equivalent

Capabilities Developed in this Course

Capability 3: Knowledge and Practice
Capability 4: Critical Thinking
Capability 5: Solution Seeking
Capability 6: Communication
Graduate Profile: Bachelor of Science

Learning Outcomes

By the end of this course, students will be able to:
  1. Quantify uncertainty and randomness by using probability. (Capability 3, 5 and 6)
  2. Recognise and use important discrete and continuous distributions and their connections . (Capability 3, 4 and 5)
  3. Compute probabilities for continuous random variables (including bivariate) by using the probability density function and the cumulative distribution function. (Capability 3 and 5)
  4. Perform hypothesis tests in a variety of situations involving both discrete and continuous random variables. (Capability 3, 4, 5 and 6)
  5. Estimate the parameters of continuous or discrete distributions by using maximum likelihood methodology. (Capability 3 and 5)
  6. Calculate expectation and variance for discrete and continuous random variables (including bivariate). (Capability 3 and 5)
  7. Transform discrete and continuous random variables (including bivariate). (Capability 3 and 5)
  8. Apply the central limit theorem (Capability 3 and 5)


Assessment Type Percentage Classification
Assignments 22% Individual Coursework
Tutorials 8% Individual Coursework
Test 20% Individual Coursework
Final Exam 50% Individual Examination
Assessment Type Learning Outcome Addressed
1 2 3 4 5 6 7 8
Final Exam

45% in the final exam as well as 50% overall is required to pass


Tuākana Science is a multi-faceted programme for Māori and Pacific students providing topic specific tutorials, one-on-one sessions, test and exam preparation and more. Explore your options at

Statistics has a Tuākana Programme where there is a workspace and a social space shared with Science Tuakana students. Tutorials and one-to-one assistance are available. Tuākana tutors/mentors work alongside the lecturer to support students with assignments and revision for the quizzes and exams. For more information and to find contact details for the Statistics Tuākana coordinator, please see

Contacts are Susan Wingfield ( and Heti Afimeimounga (

Key Topics

  • Discrete distributions
  • Statistical inference
  • Statistical regression modelling
  • Continuous distributions
  • Bivariate distributions
  • The central limit theorem

Special Requirements

The test may be held in class time. Students will be notified on Canvas about the date and time. 
It is advantageous to attend tutorials as help is available there to complete tutorial questions. (Tutorial questions are also available on Canvas)

Workload Expectations

This course is a standard 15-point course and students are expected to spend 150 hours per semester involved in each 15-point course that they are enrolled in.

For this course, a typical weekly workload includes:

  • 6 hours of lectures,
  • 2 -hour tutorial,
  • 8 hours of reading and thinking about the content,
  • 8-10 hours of work on assignments and/or test/exam preparation,
  • Note: the above is double the typical weekly workload for a typical semester as this course is taught in a condensed 6-week period.

Delivery Mode

Campus Experience

Lectures will be available as recordings.  Other learning activities including tutorials will not be available as recordings.

Attendance on campus is required for the test and exam.

Learning Resources

Course materials are made available in a learning and collaboration tool called Canvas which also includes reading lists and lecture recordings (where available).

Please remember that the recording of any class on a personal device requires the permission of the instructor.


  •  A pdf copy of the course book will be available on Canvas.

Student Feedback

During the course Class Representatives in each class can take feedback to the staff responsible for the course and staff-student consultative committees.

At the end of the course students will be invited to give feedback on the course and teaching through a tool called SET or Qualtrics. The lecturers and course co-ordinators will consider all feedback.

Your feedback helps to improve the course and its delivery for all students.

For 2024 we plan to add probability questions to the first tutorial and quiz so that the course begins with help on assumed knowledge in both mathematics and probability.

Academic Integrity

The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework as a serious academic offence. The work that a student submits for grading must be the student's own work, reflecting their learning. Where work from other sources is used, it must be properly acknowledged and referenced. This requirement also applies to sources on the internet. A student's assessed work may be reviewed for potential plagiarism or other forms of academic misconduct, using computerised detection mechanisms.

Class Representatives

Class representatives are students tasked with representing student issues to departments, faculties, and the wider university. If you have a complaint about this course, please contact your class rep who will know how to raise it in the right channels. See your departmental noticeboard for contact details for your class reps.


The content and delivery of content in this course are protected by copyright. Material belonging to others may have been used in this course and copied by and solely for the educational purposes of the University under license.

You may copy the course content for the purposes of private study or research, but you may not upload onto any third party site, make a further copy or sell, alter or further reproduce or distribute any part of the course content to another person.

Inclusive Learning

All students are asked to discuss any impairment related requirements privately, face to face and/or in written form with the course coordinator, lecturer or tutor.

Student Disability Services also provides support for students with a wide range of impairments, both visible and invisible, to succeed and excel at the University. For more information and contact details, please visit the Student Disability Services’ website

Special Circumstances

If your ability to complete assessed coursework is affected by illness or other personal circumstances outside of your control, contact a member of teaching staff as soon as possible before the assessment is due.

If your personal circumstances significantly affect your performance, or preparation, for an exam or eligible written test, refer to the University’s aegrotat or compassionate consideration page

This should be done as soon as possible and no later than seven days after the affected test or exam date.

Learning Continuity

In the event of an unexpected disruption, we undertake to maintain the continuity and standard of teaching and learning in all your courses throughout the year. If there are unexpected disruptions the University has contingency plans to ensure that access to your course continues and course assessment continues to meet the principles of the University’s assessment policy. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator/director, and if disruption occurs you should refer to the university website for information about how to proceed.

The delivery mode may change depending on COVID restrictions. Any changes will be communicated through Canvas.

Student Charter and Responsibilities

The Student Charter assumes and acknowledges that students are active participants in the learning process and that they have responsibilities to the institution and the international community of scholars. The University expects that students will act at all times in a way that demonstrates respect for the rights of other students and staff so that the learning environment is both safe and productive. For further information visit Student Charter


Elements of this outline may be subject to change. The latest information about the course will be available for enrolled students in Canvas.

In this course students may be asked to submit coursework assessments digitally. The University reserves the right to conduct scheduled tests and examinations for this course online or through the use of computers or other electronic devices. Where tests or examinations are conducted online remote invigilation arrangements may be used. In exceptional circumstances changes to elements of this course may be necessary at short notice. Students enrolled in this course will be informed of any such changes and the reasons for them, as soon as possible, through Canvas.

Published on 01/11/2023 10:23 a.m.