## Statistics 2X: Probability II STATS2005

• School: School of Mathematics and Statistics
• Credits: 10
• Level: Level 2 (SCQF level 8)
• Typically Offered: Semester 2
• Available to Visiting Students: Yes

### Short Description

This course introduces students to multivariate probability distributions and basic concepts in large sample theory;

### Timetable

Lectures: Monday and Wednesday at 9.00 am.

Workshops and drop-in help-rooms arranged via MyCampus (several groups available).

### Requirements of Entry

Required: Mathematics 1 at grade D or better.

Strongly recommended: Statistics 1Y and Statistics 1Z.

### Co-requisites

Statistics 2R: Probability

Mathematics 2A

Mathematics 2B

Mathematics 2D

### Assessment

End-of-course examination (80%); coursework (20%).

Reassessment will, generally, not be available for the coursework.

Main Assessment In: April/May

Are reassessment opportunities available for all summative assessments? No

Reassessments are normally available for all courses, except those which contribute to the Honours classification. For non Honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions for this course are described below.

Reassessment will, generally, not be available for the coursework component of this course.

### Course Aims

The aims of this course are:

■ to introduce students to multivariate probability distributions;

■ to introduce students to methods for obtaining the distribution of a sum or mean of a sequence of independent random variables;

■ to equip students to apply probability to solve problems from a wide range of disciplines;

■ to promote an interest in Probability and Statistics and hence encourage students to study more advanced courses.

### Intended Learning Outcomes of Course

By the end of this course students will be able to:

■ explain the terms joint distribution and independent random variables;

■ derive marginal and conditional distributions and their moments, and the covariance and correlation between random variables (both discrete and continuous);

■ find the distribution of functions of more than one random variable;

■ use standard methods to derive the distribution of the sum of a sequence of random variables;

■ use and derive links between different discrete and continuous distributions;

■ define and use the multivariate normal distribution and use and derive core properties such as the marginal and conditional distributions

■ state, use and derive probability inequalities such as the Chebyshev inequality;

■ state, explain and use the laws of large numbers and the central limit theorem.

### Minimum Requirement for Award of Credits

Minimum requirement as in code of assessment