Statistics
Te Tari Pāngarau me te Tatauranga
Department of Mathematics & Statistics

## STAT405 Probability and Random Processes

 First Semester
20 points

Theory and application of probability and random processes.

Students successfully completing this course will be able to demonstrate the following:

• Understanding of probability, distributions, and how this informs data analysis
• Knowledge of different paradigms for statistical inference
• Understanding of the relationship between theory and some of the most commonly used statistical modelling techniques, especially regression
• Ability to develop methods for problems without standard solutions using maximum likelihood
• Ability to apply methodology and statistical computing to analyse data using advanced regression techniques, and interpret results in a logical manner
• Autonomy and judgement in presenting results to others, including non-scientists

### Topics

• Mathematical foundations of probability theory
• Random variables and their properties
• Convergence of random variables
• Discrete time Markov processes
• Continuous time Markov processes
• Processes with continuous state space
• Diffusion processes

• Grimmett, G.R and Stirzaker, D.R. (2001) Probability and Random Processes. Oxford University Press (3rd edition)
• Guttorp, P. (2018) Stochastic modeling of scientific data. CRC press
• Billingsley, P. Statistical Inference for Markov Processes
• Jones, P.W. and Smith, P. (2017) Stochastic Processes: An Introduction. CRC press

### Prerequisites

STAT 370, MATH 202 and MATH 203

### Lecturer

Matt Parry and Martin Hazelton

### Final mark

Your final mark F in the paper will be calculated according to this formula:

F = 0.4A + 0.6E

where:

• E is the Exam mark
• A is the Assignments mark

and all quantities are expressed as percentages.

### Students must abide by the University’s Academic Integrity Policy

Academic integrity means being honest in your studying and assessments. It is the basis for ethical decision-making and behaviour in an academic context. Academic integrity is informed by the values of honesty, trust, responsibility, fairness, respect and courage.

Academic misconduct is seeking to gain for yourself, or assisting another person to gain, an academic advantage by deception or other unfair means. The most common form of academic misconduct is plagiarism.

Academic misconduct in relation to work submitted for assessment (including all course work, tests and examinations) is taken very seriously at the University of Otago.

All students have a responsibility to understand the requirements that apply to particular assessments and also to be aware of acceptable academic practice regarding the use of material prepared by others. Therefore it is important to be familiar with the rules surrounding academic misconduct at the University of Otago; they may be different from the rules in your previous place of study.

Any student involved in academic misconduct, whether intentional or arising through failure to take reasonable care, will be subject to the University’s Student Academic Misconduct Procedures which contain a range of penalties.

If you are ever in doubt concerning what may be acceptable academic practice in relation to assessment, you should clarify the situation with your lecturer before submitting the work or taking the test or examination involved.

Types of academic misconduct are as follows:

#### Plagiarism

The University makes a distinction between unintentional plagiarism (Level One) and intentional plagiarism (Level Two).

• Although not intended, unintentional plagiarism is covered by the Student Academic Misconduct Procedures. It is usually due to lack of care, naivety, and/or to a lack to understanding of acceptable academic behaviour. This kind of plagiarism can be easily avoided.
• Intentional plagiarism is gaining academic advantage by copying or paraphrasing someone elses work and presenting it as your own, or helping someone else copy your work and present it as their own. It also includes self-plagiarism which is when you use your own work in a different paper or programme without indicating the source. Intentional plagiarism is treated very seriously by the University.

#### Unauthorised Collaboration

Unauthorised Collaboration occurs when you work with, or share work with, others on an assessment which is designed as a task for individuals and in which individual answers are required. This form does not include assessment tasks where students are required or permitted to present their results as collaborative work. Nor does it preclude collaborative effort in research or study for assignments, tests or examinations; but unless it is explicitly stated otherwise, each students answers should be in their own words. If you are not sure if collaboration is allowed, check with your lecturer..

#### Impersonation

Impersonation is getting someone else to participate in any assessment on your behalf, including having someone else sit any test or examination on your behalf.

#### Falsiﬁcation

Falsiﬁcation is to falsify the results of your research; presenting as true or accurate material that you know to be false or inaccurate.

#### Use of Unauthorised Materials

Unless expressly permitted, notes, books, calculators, computers or any other material and equipment are not permitted into a test or examination. Make sure you read the examination rules carefully. If you are still not sure what you are allowed to take in, check with your lecturer.

#### Assisting Others to Commit Academic Misconduct

This includes impersonating another student in a test or examination; writing an assignment for another student; giving answers to another student in a test or examination by any direct or indirect means; and allowing another student to copy answers in a test, examination or any other assessment.

Further information

While we strive to keep details as accurate and up-to-date as possible, information given here should be regarded as provisional. Individual lecturers will confirm teaching and assessment methods.