Aims

To develop ideas and methods that are essential for the study of probability and statistics. To develop a familiarity with ideas of discrete and continuous probability models and their interpretation. To develop concepts in probability that underpin methods of statistical inference.

Module summary

The course will cover the key concepts required for further study of probability and statistics. We begin with the fundamentals of probability theory, considering probability for discrete outcomes such as National Lottery draws or poker hands. We will then move on to probability distributions and investigate how they can be used to model uncertain quantities such as the response of patients to a new treatment in a clinical trial and the occurrence of earthquakes in tectonically active regions. The module will introduce ideas of bivariate distribution and covariation, which are fundamental to many of the most useful statistical techniques.

Outline Of Syllabus

Introduction to random variation and probability including the probability axioms.

Conditional probability and independence.

Discrete probability models: the binomial, geometric and Poisson distributions. Discrete bivariate models.

Continuous probability models: the uniform, exponential and Normal distributions.

QQ-plot for Normal case. Bivariate continuous distributions.

Use of R for mathematical computing. Getting started, input and output, data types, plotting and simple calculations, control statements, functions, random variables. Use of R for illustration of fundamental concepts in probability.

Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

Assessment Rationale And Relationship

A substantial formal unseen written examination is appropriate for the assessment of the material in this module. Material on the R programming language is best assessed in a computer-based exam. The coursework assignment allows the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; it has a secondary formative purpose as well as their primary summative purpose.