# Mathematics

## MTH1004 - Probability, Statistics and Data (2019)

MODULE TITLE CREDIT VALUE Probability, Statistics and Data 30 MTH1004 Prof Peter Challenor (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 11 0
 Number of Students Taking Module (anticipated) 276
DESCRIPTION - summary of the module content

Our ability to collect and analyse data is increasingly driving our world. Statistics is concerned with both the practice of analysing data to learn about the world, and also the theory that underpins the methods and models used for data collection and analysis. This theory is itself based on probability, the mathematics of chance and uncertainty. In this module, you will learn about the mathematics of probability, and the key ideas of statistical modelling and inference, in which probability is used to quantify uncertainty. You will also gain experience of employing these ideas to analyse data using advanced statistical software.

AIMS - intentions of the module

The aim of this module is to introduce you to basic topics in probability, statistics and data analysis. This module provides the foundation for the second-year stream in Statistical Modelling and Inference, and subsequent modules in statistics in years 3 and 4.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module you should be able to:

Module Specific Skills and Knowledge:

1 demonstrate a sound understanding of selected essential topics in probability theory, including the ability to apply those concepts in tackling an appropriate range of problems;

2 demonstrate a knowledge of the basic ideas of statistical inference, including probability distributions, point and interval estimation and hypothesis tests;

3 use the computer languate R to manipulate, visualise and analyse data.

Discipline Specific Skills and Knowledge:

4 show sufficient knowledge of fundamental mathematical and statistical concepts, manipulations and results.

Personal and Key Transferable/ Employment Skills and  Knowledge:

5 reason using abstract ideas, formulate and solve problems and communicate reasoning and solutions effectively in writing;

6 work effectively as part of a small team;

7 communicate orally with team members and via a poster and report;

8 use learning resources appropriately;

9 exhibit self management and time management skills.

SYLLABUS PLAN - summary of the structure and academic content of the module

- the nature of data;

- probability;

- applications of probability;

- random variables and discrete distributions;

- statistical modelling;

- applications of discrete distributions;

- continuous random variables: the exponential, gamma, uniform and normal distributions, expectations and moments;

- bivariate and multivariate distributions;

- parametric models and estimation;

- prediction and simulation;

- application of models;

- combinations of random variables;

- transformation of random variables;

- point estimators;

- interval estimation and confidence intervals;

- hypothesis testing.

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study 89 211
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled learning and teaching activities 66 Lectures Scheduled learning and teaching activities 11 Practical classes in a computer lab Scheduled learning and teaching activities 12 Tutorials Guided independent study 211 Guided independent study

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Exercise sheets 10 x 5 hours 1-4 Tutorials
Introduction to R 10 hours 3 Feedback sheet
Draft poster 10 hours 1-6 Feedback sheet
Short project 10 hours 1-6 Feedback sheet
Test 1 hour 1-2,4-5 Marked annotated script

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams 40 60
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written exam – closed book 70 2 hours 1,2,4,5 Via SRS
Poster 10 Group Poster 1-7 Feedback sheet
Report 20 Group Project about 5 pages in length 1-7 Feedback sheet

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-reassessment
All above Written exam (100%) All August Ref/Def period

RE-ASSESSMENT NOTES

Referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

ELE – http://vle.exeter.ac.uk

Reading list for this module:

Type Author Title Edition Publisher Year ISBN Search
Set McColl, J Probability Arnold 1995 0000340614269 [Library]
CREDIT VALUE ECTS VALUE 30 15
PRE-REQUISITE MODULES None None
NQF LEVEL (FHEQ) AVAILABLE AS DISTANCE LEARNING 4 No Tuesday 10 July 2018 Thursday 27 June 2019
KEY WORDS SEARCH Probability; probability distributions; continuous and discrete random variables; moment generating function; statistics; estimation; data analysis; R.