The theory and methods of Statistics play an important role in all walks of life, society, medicine and industry. They enable important understanding to be gained and informed decisions to be made, about a population by examining only a small random sample of the members of that population. For example, to decide whether a new drug improves the symptoms of a disease in all those diagnosed as having the condition (the population), a clinical trial might be undertaken in which a sample of people who receive the new drug is compared with a sample receiving no active treatment. Such statistical inferences about a population are subject to uncertainty - what we observe in our particular sample (or samples) may not hold for the whole population. Probability theory and statistical distributions are needed to quantify this uncertainty, and assess the accuracy of our inference about the population. This module aims to lay foundations in probability and distribution theory, data analysis and the use of a statistical software package, which will be built upon in later modules.
The module begins by introducing statistical data analysis by using the freely available R package, https://cran.r-project.org/. Statistical analysis and report writing are discussed along with the use of the R software package for summarising and interpreting data.
It then formally defines probability and studies the key properties. The concepts of random variables as outcomes of random experiments are introduced and the key properties of the commonly used standard univariate random variables are studied. Emphasis is placed on learning the theories by proving key properties of each distribution.
Basic ideas of statistical inference, including techniques of point and interval estimation and hypothesis testing, are introduced and illustrated with practical examples.
One of the pre-requisites for MATH2010, MATH2011, MATH2013, MATH2040