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## MATH1710 Probability and Statistics I

### 10 creditsClass Size: 475

Module manager: Dr Matthew Aldridge
Email: M.Aldridge@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2023/24

### Pre-requisite qualifications

Grade B in A-level Mathematics or equivalent.

### This module is mutually exclusive with

 LUBS1240 Maths&Stats For Bus&Ec 1 LUBS1275 Mathematics and Statistics for Economics and Business 1A LUBS1285 Mathematics and Statistics for Economics and Business 1B

Module replaces

MATH1715

This module is 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 arguments. The key ideas of probability and random variables are discussed, including concepts of prior and posterior distributions.

### Objectives

On completion of this module, students should be able to:
(a) carry out exploratory data analysis, using a statistical package
(b) state and use the basic rules of probability
(c) understand discrete and continuous probability models
(d) understand the notions of prior and posterior probability

### Syllabus

1. Exploratory Data Analysis: numerical and graphical summaries.
2. Introduction to probability axioms, and probability rules.
3. Joint and conditional probability, independence and Bayes' formula.
4. Discrete random variables, Bernoulli trials, binomial distribution.
5. Continuous random variables. Uniform, exponential and normal distributions.
6. Models for data, and parameters.
7. Expectation and Variance.
8. Likelihood.
9. Prior and Posterior Distributions.

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 22 1.00 22.00 Tutorial 5 1.00 5.00 Private study hours 73.00 Total Contact hours 27.00 Total hours (100hr per 10 credits) 100.00

### Private study

This will include tutorial exercise sheets, lecture preparation, studying course material, using R for data analysis, revision for exams, preparing for tutorials.

### Opportunities for Formative Feedback

Fortnightly tutorials and homework sheets.

!!! In order to pass the module, students must pass the examination. !!!

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment In-course Assessment . 30.00 Total percentage (Assessment Coursework) 30.00

There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above. The assessment will cover traditional and computing exercises to help students remain up to date with learning material and account for A-level syllabus.

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 70.00 Total percentage (Assessment Exams) 70.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated