Download MA1608 Introduction to Probability and Statistics

MODULE SPECIFICATION – UNDERGRADUATE PROGRAMMES
KEY FACTS
Module name
Module code
School
Department or equivalent
UK credits
ECTS
Level
Delivery location
(partnership programmes
only)
Introduction to Probability and Statistics
MA1608
School of Engineering and Mathematical Sciences
Mathematical Sciences
15
7.5
4
MODULE SUMMARY
Module outline and aims
This module will provide you with the fundamental tools in probability and statistics which
are part of the basic knowledge required for mathematicians, and necessary for the
understanding of related modules later in the programme.
The aims of the module are to


Provide an introduction to probability.
Provide an introduction to the analysis of data and statistical modelling.
Content outline


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Ways of displaying data: bar chart, pie chart, stem-and-leaf plot, histogram.
Summary statistics: mean, median, mode, variance, quartiles.
Grouped data: summary statistics and cumulative frequencies.
Paired data: covariance and correlation, linear regression and best fit.
Randomness and the sample space; events using basic set theory.
Conditional probability and independence.
Discrete random variables, their associated statistics, and some models.
Continuous random variables: basic properties, the normal distribution and the
normal approximation to the Binomial distribution.
Expectation and variance of combinations of independent variables and of
samples.
Confidence intervals.
Parametric hypothesis testing.
WHAT WILL I BE EXPECTED TO ACHIEVE?
On successful completion of this module, you will be expected to be able to:
Knowledge and understanding:




Demonstrate an understanding of the axioms of probability and the definition of
conditional probability.
Understand the concept of a random variable and be familiar with common
distributions.
Know the definitions of common sample statistics.
Understand the theory underlying statistical techniques.
Skills:
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Construct probabilistic models appropriate to a problem described in words.
Construct statistical displays appropriate to the data.
Use Venn diagrams to illustrate probabilistic arguments.
Explain in words the results of probabilistic or statistical analysis having regard to
the situation being modelled.
Apply mathematical tools in the analysis of problems in probability or statistics.
Use statistical tables.
Test hypotheses and derive confidence intervals in well defined circumstances.
Values and attitudes:

Demonstrate awareness of the need for caution in making claims based on
statistical evidence and scepticism in interpreting the claims made by others.
HOW WILL I LEARN?
Teaching and Learning methods are designed to foster your knowledge of and
enthusiasm for the subject and stimulate engagement and participation in the learning
process. They encourage learning in depth and encourage you to reflect on and take
responsibility for your own learning and to develop your academic self-confidence.
Lectures are the principal introduction to new material. They are relatively formal in
style and are presented to the whole student. Each lecture is of 50 minutes duration
with the timetable based on units of one hour to allow for short breaks. Full, prompt
attendance is expected.
For tutorials, groups are smaller and provide opportunities for you to work on problems
and exercises connected with the module. They also provide an additional opportunity
for staff to help you with questions arising from the lectures.
In addition to the taught elements of the programme, there will be the need for private
study. This time will be spent working on background reading, revision of notes, work
on tutorial problems, and preparation of the set exercises. Key learning and teaching
resources will be put on the module website on Moodle.
Teaching pattern:
Teaching
component
Teaching
type
Contact
hours
(scheduled)
Lectures
Tutorials
Lecture
Tutorial
Totals
Placemen
t hours
20
10
Self-directed
study hours
(independent
)
100
20
0
0
Total
student
learning
hours
120
30
30
120
0
150
WHAT TYPES OF ASSESSMENT AND FEEDBACK CAN I EXPECT?
Assessments
The assessment for this module is by a 2 hour examination together with a series of set
exercises. The set exercises will normally consist of questions to be completed during
periods of self-study and a combination of different types of quizzes.
Assessment pattern:
Assessment
component
Assessment
type
Set Exercises
Set Exercises
Examination
Written Exam
Reassessment Task Written Exam
Weighting
20
80
100
Minimum
qualifying
mark
0
0
40
Pass/Fail?
N/A
N/A
N/A
Assessment criteria
Assessment Criteria are descriptions of the skills, knowledge or attributes students need
to demonstrate in order to complete an assessment successfully and Grade-Related
Criteria are descriptions of the skills, knowledge or attributes students need to
demonstrate to achieve a certain grade or mark in an assessment. Assessment Criteria
and Grade-Related Criteria for module assessments will be made available to students
prior to an assessment taking place. More information will be available from the module
leader.
Feedback on assessment
Following an assessment, students will be given their marks and feedback in line with
the Assessment Regulations and Policy. More information on the timing and type of
feedback that will be provided for each assessment will be available from the module
leader.
Assessment Regulations
The Pass mark for the module is 40%. The weighting of the different components can
also be found in the table above. The Programme Specification contains information on
what happens if you fail an assessment component or the module.
INDICATIVE READING LIST
The book chosen to accompany this module is Introduction to Probability and Statistics
by Seymour Lipschutz and John Schiller, in the Schaums Outlines series, published by
McGraw-Hill.
Alternatives are:
 Milton and Arnold: Introduction to Probability and Statistics (McGraw-Hill
International Edition)
 Clarke and Cooke: A Basic Course in Statistics by Clarke and Cooke (Arnold).
Daly, Hand, Jones, Lunn and McConway: Elements of Statistics (Addison
Wesley, Open University)
Version: 3.0
Version date: May 2016
For use from: 2016-17
Appendix: see http://www.hesa.ac.uk/content/view/1805/296/ for the full list of JACS
codes and descriptions
CODES
HESA Code
122
Description
Mathematics
Price Group
C
JACS Code
G300
Description
The study of the collection
and analysis of numerical
data.
The mathematical study of
chance.
Percentage (%)
50
G320
50