MA2500: Foundations of Probability and Statistics

School Cardiff School of Mathematics
Department Code MATHS
Module Code MA2500
External Subject Code 100406
Number of Credits 20
Level L5
Language of Delivery English
Module Leader Dr Dafydd Evans
Semester Autumn Semester
Academic Year 2022/3

Outline Description of Module

Knowledge of probability and statistics is useful in many graduate careers. This double module gives students an understanding of the principles underlying statistical methods commonly used by professional statisticians, and is intended to prepare students for a career involving statistical analysis.

The first part of the module begins with the study of probability spaces, random variables and distributions, followed by the theory of mathematical expectation and conditional expectation. We then look at moment generating functions, which are used to prove classical limit theorems such as the law of large numbers and the central limit theorem. The second part of the module begins with a study of parameter estimation, including the notions of consistency and efficiency, and an introduction to Bayesian inference. We then look at the theory of statistical hypothesis testing, focusing in particular on the likelihood ratio test and a number of different non-parametric tests.

Prerequisite Module: MA1500 Introduction to Probability Theory

Recommended Module: MA1501 Statistical Inference

On completion of the module a student should be able to

  • Understand the theoretical foundations of probability and statistics.
  • Derive relationships between different probability distributions.
  • Prove fundamental results such as the central limit theorem.
  • Explain the theoretical basis of parameter estimation and hypothesis testing

How the module will be delivered

Modules will be delivered through blended learning. You will be guided through learning activities appropriate to your module, which may include:

  • Weekly face to face classes (e.g. labs, lectures, exercise classes)
  • Electronic resources that you work through at your own pace (e.g. videos, exercise sheets, lecture notes, e-books, quizzes)

Students are also expected to undertake self-guided study throughout the duration of the module.

Skills that will be practised and developed

Skills:

An ability to apply various mathematical ideas and techniques to the study of probability and statistics.

An ability to choose appropriate statistical tests in different contexts, and to perform and interpret the results of such tests.

Transferable Skills:

Formulating problems and presenting clear solutions through logical reasoning.

Assessment Breakdown

Type % Title Duration(hrs)
Exam - Autumn Semester 100 Foundations Of Probability And Statistics 3

Syllabus content

  • Probability spaces.
  • Random variables and distributions.
  • Expectation.
  • Joint distributions.
  • Sums of random variables
  • Estimation.
  • Hypothesis testing.

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