
Module Availability 
Spring 


Assessment Pattern 
Unit(s) of Assessment

Weighting Towards
Module Mark( %)

Coursework: 23 tests / assignments

25

Exam: End of Spring semester

75

Qualifying Condition(s)
A weighted aggregate mark of 40% is required to pass the module.




Module Overview 



Prerequisites/Corequisites 
None. 


Module Aims 
This module introduces students to mathematical probability theory and its applications to statistics. 


Learning Outcomes 
By the end of this module a student should be able to:
 Apply basic results in probability, distribution theory and statistical inference to straightforward problems.
 Use the statistical package R to perform statistical calculations and to produce numerical and graphical data summaries.




Module Content 
Probability
 Probability theory, including Bayes' Theorem.
 Some standard discrete distributions: binomial, Poisson, hypergeometric, and continuous distributions: normal, exponential.
 Expectation and moments.
 Probability generating functions.
 Sums of random variables.
 Statement of the central limit theorem.
 Sampling distributions.
 Inference for means and proportions.
 Estimation: unbiased estimators; maximum likelihood and moment estimators.
 Hypothesis testing: Type I and II errors, power.
 Chisquared Goodness of fit.
 An Introduction to R.




Methods of Teaching/Learning 
Teaching is by lectures, tutorials, computer lab sessions and tests. Learning takes place through lectures, tutorials, computer lab sessions, tests and exercise sheets.
40 hours of lectures, tutorials and lab sessions over 12 weeks in the Spring semester.



Selected Texts/Journals 
Recommended Reading:
 G.M. Clarke and D. Cooke, A Basic Course in Statistics, Arnold
 John E. Freund, Mathematical Statistics with Applications, Prentice Hall




Last Updated 
October 10 
