## MATH4PT Probability Theory

First Semester |

The genuine goal of probability theory is to provide mathematical methods for describing and analysing experiments with random output. In the 1930s, the Russian mathematician Andrey N. Kolmogorov suggested to formalize the study of such experiments by using measure theory. This led to an enormous development of the understanding of uncertainty.

In this lecture we aim to introduce the basic concepts of modern probability theory and to present and prove some of its fundamental results. We will mainly concentrate on the behaviour of sequences of independent random variables: the mathematical model for an infinite series of experiments that do not influence each other.

### Prerequisites

MATH4MI Measure and Integration

### Lecturer

Petru A. Cioica-Licht (Room 212, phone 479 7783, email: pcioica@maths.otago.ac.nz)

### Lecture times (intended)

**Start:** Wednesday, April 26th, 3-5 pm.

Then, twice a week until the end of the semester:

- Mondays, 9-11 am and Wednesdays, 3-5 pm.

### Further Reading

- P. Billingsley,
*Probability and Measures*, J. Wiley & Sons, New York, 1995. - H. Bauer,
*Probability Theory and Elements of Measure Theory*, 2nd English ed., Academic Press, London, 1981.

### Assessment

Short weekly assignments

### Final mark

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

**F = min(100, max(E, 0.4E + 0.6min(A, 125)))**

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 endeavours at the University of Otago are built upon an essential commitment to academic integrity.**

The two most common forms of academic misconduct are *plagiarism* and *unauthorised collaboration*.

#### Academic misconduct: **Plagiarism**

Plagiarism is defined as:

- Copying or paraphrasing another person’s work and presenting it as your own.
- Being party to someone else’s plagiarism by letting them copy your work or helping them to copy the work of someone else without acknowledgement.
- Using your own work in another situation, such as for the assessment of a different paper or program, without indicating the source.
- Plagiarism can be unintentional or intentional. Even if it is unintentional, it is still considered to be plagiarism.

All students have a responsibility to be aware of acceptable academic practice in relation to the use of material prepared by others and are expected to take all steps reasonably necessary to ensure no breach of acceptable academic practice occurs. You should also be aware that plagiarism is easy to detect and the University has policies in place to deal with it.

#### Academic misconduct: **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 student’s answers should be in their own words. If you are not sure if collaboration is allowed, check with your lecturer.