# Probability and Statistical Analysis

## Course summary

Course code: STAT1025
Level: 4
Credits: 30
School: Architecture, Computing and Hums
Department: Mathematical Sciences
Course Coordinator(s): Ana Paula Palacios / Timothy Reis

## Specification

### Pre and co requisites

AS Level Maths or equivalent.

### Aims

It is important to have an understanding of the way data can be presented and generated by simple probability models. The course will introduce the ideas of statistical inference and the use of simple statistical hypothesis tests. The aim of the course is to provide students with the ability to display and describe data sets using appropriate software, to enable students to understand elementary probability theory and to provide students with the ability to use the logic of statistical inference.

### Learning outcomes

On successful completion of this course a student will be able to:

1. Be familiar with the principles of descriptive statistics and be able to demonstrate an understanding of the use of simple probability theory and models.
2. Have a good understanding of the principles of statistical inference and hypothesis testing.
3. Be able to use simple non-parametric statistical tests.
4. Be aware of the use of correlation and simple linear regression.
5. Be able to use appropriate software for simple data analysis and interpret results.
6. Be able to appreciate disciplines and forms of professional practice beyond statistics and draw connections between them.

### Indicative content

Descriptive statistics: Bar charts, histograms, stem & leaf diagrams etc; mean, median, mode, standard deviation, inter-quartile range, etc. Basic data analysis using appropriate software (e.g. Minitab, Spreadsheets). Elementary probability: random variables (pdf, cdf), discrete distributions (Binomial, Poisson, Geometric), continuous univariate distributions (Normal, Exponential, Uniform, t, Chi-square), Laws of Expectation and Variance. Elementary inference (including t-tests, chi-squared, F-test) and Hypothesis testing. Type I and Type II errors. Non-parametric tests including Sign, Wilcoxon, Mann-Whitney, Kolmogorov-Smirnov and Rank correlation. Correlation and simple linear regression (least squares).

### Teaching and learning activity

Concepts, methods and basic conclusions will be introduced and explained in lectures.
Problem solving and technique training will be done through tutorials.
Practical work using statistical software will be done through laboratory sessions.

### Assessment

Summative assessment:
Coursework 1 - 25%
An individual coursework assessing learning outcomes 1, 2, 5 and 6.

Coursework 2 - 25%
An individual coursework assessing learning outcomes 1, 2, 3, 4, 5 and 6.

Exam - 50%
3 hours exam assessing learning outcomes 1-6.

Formative assessment: Weekly tutorial exercises