ST1PSNU-Probability and Statistics

Module Provider: Mathematics and Statistics
Number of credits: 20 [10 ECTS credits]
Level:4
Terms in which taught: Spring term module
Pre-requisites:
Non-modular pre-requisites:
Co-requisites:
Modules excluded:
Current from: 2021/2

Module Convenor: Dr Karen Poulter
Email: k.l.poulter@reading.ac.uk

Type of module:

Summary module description:

This module provides an introduction to probability and probability distributions, and to fundamental techniques for statistical inference, and for the analysis of data from observational studies, with a focus on regression and hypothesis testing.

The Module lead at NUIST is Dr Kai Zhao.

Aims:

The first half of this module provides an introduction to probability, a subject that underlies all statistical methods. Topics covered include the definition and measurement of uncertainty, the manipulation of probability statements and an introduction to both discrete and continuous probability distributions, including the role of the normal distribution. The second half of this module introduces some fundamental techniques for statistical inference, including estimation of confidence intervals and hypothesis tests. It also illustrates statistical modelling. Some simple models will be described and their role in data analysis illustrated.

Assessable learning outcomes:

On completion of this module students will have acquired:

• familiarity with the key concepts of probability;


• the ability to calculate and manipulate probabilities in simple problems;


• awareness of the concept of a random variable and its properties;


• an understanding of the applicability of some standard discrete and continuous probability distributions;


• the ability to draw inferences about a populat ion from sample data using estimation, confidence intervals and hypothesis tests and an ability for identifying when to use a given method;


• the ability to analyse categorical data;


• knowledge of the nature of a statistical model and the strength of the fit;


• the ability to fit a straight line to data, and to perform transformations when necessary;


• the ability to select and apply appropriate methods for carrying out data analysis;

Additional outcomes:

Outline content:

Views of probability; definitions of sample spaces, outcomes and events; calculating probabilities for problems with equally likely outcomes; the axioms of probability; notions of conditional probability and independence; the law of total probability and Bayes' theorem. - An introduction to discrete random variables and their properties, including Bernoulli, binomial, negative binomial, geometric, hypergeometric and Poisson random variables. - An introduction to continuous random variable s and their properties, including the uniform exponential, normal, lognormal, beta and gamma distributions. - Applications of probability, e.g. forensics, medicine, insurance, quality control and the environment. - Summary statistics, transformations and the graphical display of data. - Sampling distributions. - Confidence intervals for population means, variances and proportions in one and two samples. - Hypothesis test on one and two samples. - Categorical data analysis. Contingency tables; th e chi-squared test. - The simple linear regression model; fitting a straight line; testing the significance of a regression relationship; analysis of variance.

Brief description of teaching and learning methods:

Lectures, supported by problem sheets.