Download AM20RA Real Analysis

AM10SP
Level: 4
STATISTICS AND PROBABILITY
Credits: 10
Teaching Period: 1
Module Tutors: Dr J van Mourik
Aims
Students should understand the general principles of probability and statistics.
They should be able to:

solve problems concerning elementary probability and random variables

summarise and present data in a meaningful way.

calculate confidence limits for sampled data

perform tests of hypotheses concerning the mean, variance, goodness of fit, and
contingency tables.

perform linear regression.
Content:
Probability:
1. An introduction to probability:
Sample description spaces; events spaces; Venn diagrams; Combinatorics. The axioms of
probability. Definition and rules for combining probabilities.
2. Probability density functions: definition, cumulative, joint, marginal, independence, discrete
and continuous random variables.
Statistics:
3. Methods for summarising the data; histograms, measures of location, measures of central
tendency, measures of spread.
4. Bias, minimum variance.
5. Estimation. Sampling distributions of x and S2. Confidence limits. Tests of hypothesis
concerning the mean. Test of hypotheses concerning the variance. The χ 2 test for
goodness of fit and contingency tables.
6. An introduction to covariance and correlation and linear regression: model fitting and
significance tests.
Teaching:
Lectures 22 hours
Tutorials 11 hours
Coursework, further study and examination 67 hours
Assessment
1 Class Test (1 hour)
10% TBC
1 Coursework
10% To be handed in to the School Coursework Office MB133
Examination (1.5 hours) 80% January Examination
Feedback on the module will be given via a Class Test/Coursework Mark.
All provisional marks will be available within 4 weeks.
Feedback from the Class Test, Coursework and the Examination will take the form of a mark.
In the case of the Class Test/coursework worked solutions will be provided.
Module outcomes
What the student should gain from successful completion of the
module
Knowledge and Understanding
1. Understand the underlying principles of probability and
statistics.
2. Understand the key methods to analyse and present
data.
Intellectual Skills
1. Ability to recognise the situations in which techniques
from probability and/or statistics are applicable.
2. Ability to select the correct method.
3. Ability to execute the method.
Teaching/Learning
Methods
Assessment
Methods
Lectures/Tutorials
Examination/
Coursework
Lectures/Tutorials
Examination/
Coursework
SEAS, Aston University – AM Module Specification 2011/12
Last update 05/09/11
Professional/Subject-Specific Skills
1. Calculate the probability for events, using the elementary
definitions of probability
2. Calculate (joint) expectation values for discrete and
continuous random variables, determine their
independence.
3. Summarise and present data in a meaningful way.
4. Calculate confidence limits for sampled data.
5. Perform tests of hypotheses concerning the mean,
variance, goodness of fit and contingency tables.
6. Perform linear regression.
Lectures/Tutorials
Examination/
Coursework
Lectures/Tutorials
Examination/
Coursework
Transferable Skills
1. Presentation, time management
Reading List: Chatfield, C. (1995) Statistics for Technology. 3rd Edition Revised. CRC Press.
Devore, J. (1995) Probability and Statistics for Engineering and the Sciences. 4th Edition.
Wadsworth Publishing: California. (Accompanying software available at the Loans Counter).
Lipschutz and Schiller (1998), Introduction to probability and statistics, Schaum’s outline
series, McGraw-Hill.
Stirzaker D. (1999), Probability and Random Variables: a Beginner's Guide, Cambridge UP.
Walpole, R. E. Myers R.H. and Myers, S. L. (1998) Probability and Statistics for Engineers
and Scientists. 6th Edition. Prentice and Hall: London.
Co-requisites: Transition Mathematics (AM10TM)
SEAS, Aston University – AM Module Specification 2011/12
Last update 05/09/11