2024/25 Undergraduate Module Catalogue

MATH1700 Probability and Statistics

20 creditsClass Size: 490

Module manager: Prof. Charles Taylor; Amanda Turner
Email: C.C.Taylor@leeds.ac.uk; A.Turner5@leeds.ac.uk

Taught: Semesters 1 & 2 (Sep to Jun) View Timetable

Year running 2024/25

Pre-requisite qualifications

Grade B in A-level Mathematics or equivalent.

This module is not approved as a discovery module

Module summary

'Probability is basically common sense reduced to calculation; it makes us appreciate with exactitude what reasonable minds feel by a sort of instinct.' So said Laplace. In the modern scientific and technological world, it is even more important to understand probabilistic and statistical arguments. This module will introduce students to key ideas in both areas, with probability forming the theoretical basis for statistical tests and inference.

Objectives

This module will introduce students to the key ideas in probability theory and statistical analysis.

Learning outcomes
On successful completion of the module students will have demonstrated the following learning outcomes relevant to the subject:
1. carry out exploratory data analysis using a statistical package
2. state and use the basic rules of probability
3. understand discrete and continuous probability models
4. understand the notions of prior and posterior probability
5. describe properties of key distributions and understand simple inference
6. carry out appropriate hypothesis tests, with the aid of a statistical package
7. carry out inference on proportions
8. carry out chi-squared tests
9. understand and carry out simple linear regression

Skills learning outcomes
SLO1. Communicate information about data.
SLO2. Use statistics packages to analyse data and conduct statistical tests.
SLO3. Understand important and critical concepts of probability and chance.
SLO4. Use technology appropriately in your work and studies.

Syllabus

The following topics will be covered:
1. Exploratory data analysis: numerical and graphical summaries
2. The R programming language
3. Probability axioms and rules
4. Independence, conditional probability and Bayes' theorem
5. Discrete random variables including Bernoulli trial, binomial, geometric and Poisson distributions
6. Continuous random variables, including exponential and normal distributions
7. Expectation and variance
8. Multiple random variables: covariance, correlation, joint distributions, expectation and variance of linear combinations
9. Law of large numbers and central limit theorem
10. Introduction to Bayesian statistics: prior and posterior distributions
11. Parametric distributions as models for data
12. Point estimation, including by maximum likelihood estimation
13. Confidence intervals, including for the for mean with variance known and unknown
14. p-values and hypothesis testing for means: z-test and t-test
15. Inference for two populations: independent samples and paired samples.
16. Binary data: estimation and large-sample confidence interval for a proportion, and hypothesis testing for one or two proportions
17. Simple least-squares linear regression and inference
18. Chi-squared tests: goodness-of-fit tests and contingency tables

Methods of Assessment

We are currently refreshing our modules to make sure students have the best possible experience. Full assessment details for this module are not available before the start of the academic year, at which time details of the assessment(s) will be provided.

Assessment for this module will consist of;

2 x Portfolio of assessed questions and statistical report
2 x In-person open book exam

Teaching methods

Delivery type	Number	Length hours	Student hours
Lectures	44	1.00	44.00
seminars	10	1.00	10.00
Practicals	4	1.00	4.00
Independent online learning hours			46.00
Private study hours			96.00
Total Contact hours			58.00
Total hours (100hr per 10 credits)			200.00

Opportunities for Formative Feedback

Regular example sheets.

Reading list

The reading list is available from the Library website

Last updated: 26/09/2024 11:47:48

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