UNIVERSITY OF KENT
MODULE SPECIFICATION
SECTION 1: MODULE SPECIFICATIONS
1.
Title of the module : Probability and Statistics for Actuarial Science (MA319)
2.
School or partner institution which will be responsible for management of the module
School of Mathematics, Statistics and Actuarial Science
3.
Start date of the module September 2005 (revised version start date September 2014)
4.
The number of students expected to take the module: about 90 students
5.
Modules to be withdrawn on the introduction of this proposed module and consultation with other
relevant Schools and Faculties regarding the withdrawal
None
6.
The level of the module (e.g. Certificate [C], Intermediate [I], Honours [H] or Postgraduate [M]): C
7.
The number of credits and the ECTS value which the module represents : 15 (ECTS 7.5)
8.
Which term(s) the module is to be taught in (or other teaching pattern): Autumn term
9.
Prerequisite and co-requisite modules:
Prerequisite modules: Students need to have covered material equivalent to that in A-level
Mathematics. There are no University-level pre-requisites.
Co-requisite modules: MA321 (Calculus and Mathematical Modelling)
10. The programmes of study to which the module contributes
BSc (Hons) Actuarial Science (including programme with a year in industry), PDip Actuarial Science
11. The intended subject specific learning outcomes
On successful completion of this module students will:
a) have gained an understanding of the basic concepts of probability and statistics;
b) have established a framework of core statistical material relevant to their degree programme,
and which is also appropriate for later statistics modules students may need to study as part of
their degree;
c) be proficient in the main statistical ideas and techniques introduced in the course;
d) have some appreciation of ways of examining data, both at the exploratory stage through
graphical representations and numerical summaries, and more formally through techniques of
statistical inference;
e) be able to handle and analyse data using the statistical package MINITAB;
f) have some appreciation of how statistics is used in practice.
g) have an appreciation of how the statistical procedures covered are derived and their validity
12. The intended generic learning outcomes
Students who successfully complete this module will:
a) have begun to develop a logical, mathematical approach to solving problems;
b) have enhanced their ability to work with relatively little guidance;
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c) have gained organisational and study skills;
d) be able to use information technology for data analysis and presentation.
On successful completion of the module, students will also have improved their key skills in written
communication, numeracy, computing and problem solving.
13. Synopsis of the curriculum
Probability. Concepts of experiment, event, outcome and sample space. Venn diagrams. Certain and
impossible events. Union, intersection and complement of events. Mutually exclusive events;
Mutually exhaustive events. Axioms of probability, with interpretations. Independence. Addition and
multiplication laws. Marginal, conditional and joint probabilities. Law of total probability, Bayes’
theorem.
Discrete and continuous random variables. Concept of random variable (r.v.): classification of r.vs.;
discrete and continuous r.vs. Cumulative distribution function, probability and probability density
functions. Expectation and variance.
Distributions. Binomial, Poisson, geometric distributions; uniform, Normal and exponential
distributions. Central limit theorem. Introduction to generating functions.
Graphical representations of data. Stem-and leaf plots. Bar charts. Histograms. Cumulative
frequency plots. Scatterplots. Box-and-whisker plots.
Numerical summaries of data. Order statistics. Sample mean. Median. Trimmed mean. Mode.
Quartiles. Range. Mean deviation. Sample variance and standard deviation.
Distributions widely used in statistics. Distributions based on random sampling from Normal
distributions: χ² distribution, t-distribution, F-distribution.
Sampling distributions. Definition. Standard error. Sampling distribution of X. Sampling distribution of
the sample proportion. Sampling distribution of S2 for Normal sample.
Point estimation. Principles. Unbiased estimators. Bias
Interval estimation. Concept. Procedures for random samples from Normal distribution: confidence
interval for μ, σ2 known; confidence interval for μ, σ2 unknown; confidence interval for σ2.
Confidence interval for a proportion, for large n. Choosing the sample size. One-sided confidence
intervals.
Hypothesis testing. Testing hypotheses for μ, σ2 known. Type I and II errors. Size. p-values. Onetailed tests. Power function. Testing hypotheses for μ, σ2 unknown. Testing hypotheses for σ2 for
normal data. Testing hypotheses for a proportion with large n.
Two-sample problems. Comparing means with known variances – hypothesis test and confidence
interval. Comparing means with unknown variances – hypothesis tests and confidence intervals.
Inferences about the ration of 2 variances – hypothesis test and confidence interval. Inferences for
the difference between 2 proportions – hypothesis test and confidence interval.
Association between variables. Product moment and rank correlation coefficients. Two-way
contingency tables. χ² test of independence.
Introduction to nonparametric procedures. χ² goodness of fit test for fully specified H0. χ² goodness
of fit test for more general H0.
14. Indicative Reading List
S Ross. A first course in probability. (4th ed. Prentice Hall, 1994)
J Devore and R Peck. Introductory Statistics. (West. 1990) (especially recommended for students
who have not done statistics before)
F Daly et al. Elements of Statistics. (The Open University. 1995)
GM Clarke & D Cooke. A Basic Course in Statistics. (5th edition. Arnold. 2004)
Formulae and Tables for Examinations of the Institute and Faculty of Actuaries
15. Learning and Teaching Methods, including the nature and number of contact hours and the total
study hours which will be expected of students, and how these relate to achievement of the intended
module learning outcomes.
Number of contact hours: 48, consisting of 36 lectures, 2 formal computing sessions and 10 exercise
classes.
Number of independent learning hours: 102.
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Total study hours: 150.
The lectures introduce the students to the basic concepts of probability and statistics. The material is
related to real data at every stage and MINITAB is used to provide statistical computing facilities for
all the material studied. Probability, data description and data summarisation techniques are studied,
together with the main methods of statistical inference.
Lectures contain numerous worked examples to illustrate the theoretical techniques and concepts in
the curriculum. They address subject specific learning outcomes 11(a)-(d),(f),(g) and generic learning
outcomes 12(a). The exercise sheets, which students are expected to attempt, aim to reinforce the
lecture material, in addition to giving students practice in the various statistical techniques. In addition
to the exercise sheets, students also work on several practical problems for which they need to use
MINITAB. These practical problems are intended to give further reinforcement of the technical
material, as well as illustrating how statistics is used in practice.
Regular exercise classes are held during which students work on specified exercises with the module
lecturers and other staff on hand to help with any problems. This provides each student with one-toone help when needed.
Students work through worksheets which demonstrate how the statistical techniques introduced in the
module can be implemented in MINITAB. The exercise classes and computing sessions address
subject specific learning outcomes 11(a)-(g) and generic learning outcomes 12(a)-(d).
16. Assessment methods and how these relate to testing achievement of the intended module learning
outcomes
The module will be assessed by examination (90%) and coursework (10%).
Coursework: Exercises will be given on individual components of the syllabus, to be worked on during
the exercise classes with the module lecturers and other staff on hand to help with any problems and
completed outside contact hours. The exercises consist of questions requiring mathematical
manipulations and solution to numerical problems. Required answers will vary in length. The
exercises assess subject specific learning outcomes 11(a)-(g) and generic learning outcomes 12(a)(d).
Examination: One 2-hour written exam in the Summer term. The examination paper will consist of
theoretical, manipulative and numerical problems requiring answers of varying length, testing subject
specific learning outcomes 11(a)-(d),(f),(g) and generic learning outcomes 12(a)-(c).
17. Implications for learning resources, including staff, library, IT and space
This module has been developed from existing modules and there are no further resource
implications.
18. The School recognises and has embedded the expectations of current disability equality legislation,
and supports students with a declared disability or special educational need in its teaching. Within this
module we will make reasonable adjustments wherever necessary, including additional or substitute
materials, teaching modes or assessment methods for students who have declared and discussed
their learning support needs. Arrangements for students with declared disabilities will be made on an
individual basis, in consultation with the University’s disability/dyslexia support service, and specialist
support will be provided where needed.
19. Campus where module will be delivered: Canterbury
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UNIVERSITY OF KENT
SECTION 2: MODULE IS PART OF A PROGRAMME OF STUDY IN A UNIVERSITY SCHOOL
Statement by the School Director of Learning and Teaching/School Director of Graduate Studies
(as appropriate): "I confirm I have been consulted on the above module proposal and have given advice
on the correct procedures and required content of module proposals"
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Director of Learning and Teaching/Director of
Graduate Studies (delete as applicable)
Date
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Print Name
Statement by the Head of School: "I confirm that the School has approved the introduction of the
module and, where the module is proposed by School staff, will be responsible for its resourcing"
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Head of School
Date
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Print Name
Module Specification Template
Last updated February 2013
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