Unit of study_

# STAT2011: Probability and Estimation Theory

## Overview

This unit provides an introduction to probability, the concept of random variables, special distributions including the Binomial, Hypergeometric, Poisson, Normal, Geometric and Gamma and to statistical estimation. This unit will investigate univariate techniques in data analysis and for the most common statistical distributions that are used to model patterns of variability. You will learn the method of moments and maximum likelihood techniques for fitting statistical distributions to data. The unit will have weekly computer classes where you will learn to use a statistical computing package to perform simulations and carry out computer intensive estimation techniques like the bootstrap method. By doing this unit you will develop your statistical modelling skills and it will prepare you to learn more complicated statistical models.

### Details

Academic unit Mathematics and Statistics Academic Operations STAT2011 Probability and Estimation Theory Semester 1, 2023 Normal day Remote 6

### Enrolment rules

 Prohibitions ? STAT2911 (MATH1X21 or MATH1931 or MATH1X01 or MATH1906 or MATH1011) and (DATA1X01 or MATH10X5 or MATH1905 or STAT1021 or ECMT1010 or BUSS1020) None Yes

### Teaching staff and contact details

Coordinator Clara Grazian, clara.grazian@sydney.edu.au Clara Grazian

## Assessment

Type Description Weight Due Length
Supervised exam

Final exam
60% Formal exam period 2 hours
Outcomes assessed:
Online submission of 3 computer lab reports
5% Multiple weeks Variable
Outcomes assessed:
Tutorial quiz Quiz 1
Online quiz 1, during last lecture of Week 5
10% Week 05
Due date: 22 Mar 2023 at 13:00
45 mins
Outcomes assessed:
Tutorial quiz Quiz 2
Online quiz 2, during last lecture of Week 11
10% Week 11
Due date: 10 May 2023 at 13:00
45 mins
Outcomes assessed:
Assignment Assignment
Assignment
15% Week 12
Due date: 19 May 2023 at 23:59
1 week
Outcomes assessed:

Detailed information for each assessment can be found on Canvas.

• Final exam: If a second replacement exam is required, this exam may be delivered via an alternative assessment method, such as a viva voce (oral exam). The alternative assessment will meet the same learning outcomes as the original exam. The format of the alternative assessment will be determined by the unit coordinator.

### Assessment criteria

Result name

Mark range

Description

High distinction

85 - 100

At HD level, a student demonstrates a flair for the subject as well as a detailed and comprehensive understanding of the unit material. A ‘High Distinction’ reflects exceptional achievement and is awarded to a student who demonstrates the ability to apply their subject knowledge and understanding to produce original solutions for novel or highly complex problems and/or comprehensive critical discussions of theoretical concepts.

Distinction

75 - 84

At DI level, a student demonstrates an aptitude for the subject and a well-developed understanding of the unit material. A ‘Distinction’ reflects excellent achievement and is awarded to a student who demonstrates an ability to apply their subject knowledge and understanding of the subject to produce good solutions for challenging problems and/or a reasonably well-developed critical analysis of theoretical concepts.

Credit

65 - 74

At CR level, a student demonstrates a good command and knowledge of the unit material. A ‘Credit’ reflects solid achievement and is awarded to a student who has a broad general understanding of the unit material and can solve routine problems and/or identify and superficially discuss theoretical concepts.

Pass

50 - 64

At PS level, a student demonstrates proficiency in the unit material. A ‘Pass’ reflects satisfactory achievement and is awarded to a student who has threshold knowledge.

Fail

0 - 49

When you don’t meet the learning outcomes of the unit to a satisfactory standard.

### Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

• Deduction of 5% of the maximum mark for each calendar day after the due date.
• After ten calendar days late, a mark of zero will be awarded.

### Special consideration

If you experience short-term circumstances beyond your control, such as illness, injury or misadventure or if you have essential commitments which impact your preparation or performance in an assessment, you may be eligible for special consideration or special arrangements.

The Current Student website provides information on academic honesty, academic dishonesty, and the resources available to all students.

The University expects students and staff to act ethically and honestly and will treat all allegations of academic dishonesty or plagiarism seriously.

We use similarity detection software to detect potential instances of plagiarism or other forms of academic dishonesty. If such matches indicate evidence of plagiarism or other forms of dishonesty, your teacher is required to report your work for further investigation.

## Weekly schedule

WK Topic Learning activity Learning outcomes
Week 01 1. Introduction; 2. Sample spaces and the algebra sets; 3. The probability function; 4. Conditional probability Lecture and tutorial (5 hr)
Week 02 1. Independence; 2. Combinatorics Lecture and tutorial (5 hr)
Week 03 1. Combinatorial probability; 2. Discrete random variables; 3. Expected value and variance Lecture and tutorial (5 hr)
Week 04 1. Binomial random variables 2. Poisson random variables 2. Hypergeometric random variables Lecture and tutorial (5 hr)
Week 05 1. Other discrete random variables 2. Continuous random variables 3. Expected value and variance 4. Uniform random variables Lecture and tutorial (5 hr)
Week 06 1. Normal random variables 2. Gamma random variables Lecture and tutorial (5 hr)
Week 07 1. Joint densities; 2. Transforming and combining random variables; Lecture and tutorial (5 hr)
Week 08 1. Order statistics 2. Conditional densities 3. Moment generating function Lecture and tutorial (5 hr)
Week 09 1. Estimation theory Lecture and tutorial (5 hr)
Week 10 1. Estimating parameters Lecture and tutorial (5 hr)
Week 11 1. Interval estimation Lecture and tutorial (5 hr)
Week 12 1. Properties of estimation Lecture and tutorial (5 hr)
Week 13 Revision Lecture and tutorial (5 hr)
Weekly Computer lab Computer laboratory (1 hr)

### Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

The formal textbooks for the course are

Larsen, R. J., & Marx, M. L. (2005). An introduction to mathematical statistics. Prentice Hall.

OR

Ross, S. M. (2019). A first course in probability. Boston: Pearson.

(You can choose one or the other – notes are based on both).

## Learning outcomes

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University’s graduate qualities and are assessed as part of the curriculum.

At the completion of this unit, you should be able to:

• LO1. construct appropriate statistical models involving random variables for a range of modelling scenarios. Compute (or approximate with a computer if necessary) numerical characteristics of random variables in these models such as probabilities, expectations and variances
• LO2. fit such models in outcome 1. to data (as appropriate) by estimating any unknown parameters
• LO3. compute appropriate (both theoretically and computationally derived) measures of uncertainty for any parameter estimates
• LO4. assess the goodness of fit (as appropriate) of a fitted model
• LO5. apply certain mathematical results (e.g. inequalities, limiting results) to problems relating to statistical estimation theory
• LO6. prove certain mathematical results (e.g. inequalities, limiting results) used in the course.

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

 GQ1 Depth of disciplinary expertise Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline. GQ2 Critical thinking and problem solving Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem. GQ3 Oral and written communication Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context. GQ4 Information and digital literacy Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies. GQ5 Inventiveness Generating novel ideas and solutions. GQ6 Cultural competence Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues. GQ7 Interdisciplinary effectiveness Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries. GQ8 Integrated professional, ethical, and personal identity An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context. GQ9 Influence Engaging others in a process, idea or vision.

### Outcome map

GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9

## Closing the loop

No changes have been made since this unit was last offered

### Work, health and safety

We are governed by the Work Health and Safety Act 2011, Work Health and Safety Regulation 2011 and Codes of Practice. Penalties for non-compliance have increased. Everyone has a responsibility for health and safety at work. The University’s Work Health and Safety policy explains the responsibilities and expectations of workers and others, and the procedures for managing WHS risks associated with University activities.

General Laboratory Safety Rules

• No eating or drinking is allowed in any laboratory under any circumstances
• A laboratory coat and closed-toe shoes are mandatory