## ST1PS-Probability and Statistics

Module Provider: Mathematics and Statistics
Number of credits: 20 [10 ECTS credits]
Level:4
Terms in which taught: Autumn / Spring / Summer module
Pre-requisites:
Non-modular pre-requisites: A level Mathematics Grade B or higher
Co-requisites: MA1CA Calculus or CS1MA20 Mathematics and Computation
Modules excluded:
Current from: 2020/1

Module Convenor: Dr Karen Poulter

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.

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. The use of a software package for performing the techniques will be described and 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 carry out statistical analyses using a computing package;

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

• the ability to work effectively in a statistics project team and to communicate the results of a statistical analysis.

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 ra ndom variables 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. Contingen cy tables; the 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 tutorials, practicals and problem sheets.

Contact hours:
 Autumn Spring Summer Lectures 20 17 4 Seminars 2 Tutorials 9 6 Practicals classes and workshops 4 Guided independent study: 69 69 Total hours by term 98 98 4 Total hours for module 200

Summative Assessment Methods:
 Method Percentage Written exam 70 Report 15 Oral assessment and presentation 5 Set exercise 10

Summative assessment- Examinations:
3 hours.

Summative assessment- Coursework and in-class tests:

Two assignments, one group data analysis report and presentation, and one examination.

Formative assessment methods:
Problem sheets.

Penalties for late submission:

The Module Convenor will apply the following penalties for work submitted late:

• where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of five working days;
• where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.
The University policy statement on penalties for late submission can be found at: http://www.reading.ac.uk/web/FILES/qualitysupport/penaltiesforlatesubmission.pdf
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Assessment requirements for a pass:
A mark of 40% overall.

Reassessment arrangements:

One examination paper of 3 hours duration in August/September - the resit module mark will be the higher of the exam mark (100% exam) and the exam mark plus previous coursework (including presentation) marks (70% exam, 30% coursework).