# Statistics BSc/MSci

## Principles of Probability and Statistics STATS4047

• School: School of Mathematics and Statistics
• Credits: 10
• Level: Level 4 (SCQF level 10)
• Typically Offered: Semester 1
• Available to Visiting Students: Yes

### Short Description

This course establishes crucial concepts and asymptotic results that are widely relied upon in probability and statistics. These include convergence in distribution and the Central Limit Theorem for probability, and optimal properties of estimators, particularly maximum-likelihood estimators, in statistics.

### Timetable

20 lectures (2 each week)

5 tutorials (fortnightly throughout the semester)

### Excluded Courses

STATS5022 Principles of Probability and Statistics (Level M)

### Assessment

90-minute, end-of-course examination (100%)

Main Assessment In: April/May

Are reassessment opportunities available for all summative assessments? Not applicable

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.

### Course Aims

The aims of this course are:

■ to introduce and discuss the concept of convergence in the theory of random variables;

■ to establish the laws of large numbers and the Central Limit Theorem;

■ to discuss optimal properties of point estimators;

■ to establish the large-sample properties of maximum-likelihood estimation.

■ to introduce students to the EM algorithm

### Intended Learning Outcomes of Course

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

■ describe and contrast convergence in probability, convergence in distribution, convergence in quadratic mean and almost sure convergence;

■ state, use and prove various probabilistic inequalities;

■ state, prove and use the Weak Law of Large Numbers and the Central Limit Theorem;

■ state and discuss optimal properties of point estimators;

■ state, prove and use the Rao-Blackwell Theorem and the Cramer-Rao lower bound;

■ state, prove and apply general asymptotic properties of maximum-likelihood estimators;

■ construct an EM algorithm for various missing data problems.

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### Minimum Requirement for Award of Credits

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.