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Module DescriptorSchool of Computer Science and Statistics

Module CodeST2005
Module NameST2005 APPLIED PROBABILITY II
Module Short Title
ECTS5
Semester TaughtSemester 2
Contact Hours3 lectures per week including some tutorials and software labs
Module PersonnelLecturer – Dr Jason Wyse
Learning Outcomes

At the end of this module, students should be able to:

  • Derive confidence intervals and hypothesis tests for means and variances
  • Derive prediction intervals for simple statistical models and explain how they differ from confidence intervals
  • Define maximum likelihood estimates and how compute them
  • Implement a bootstrap to construct confidence intervals
  • Construct a q-q plot and use simple transformations of data that can make it more normally distributed
  • Construct a probability plot for any given distribution where its distribution function is known
  • Calculate the properties of multivariate distributions
  • Derive marginal and conditional probabilities of the bivariate normal distribution  
Learning Aims

This module will develop several important ideas in statistical analysis making use of some of the ideas introduced in ST2004.  It acts as a bridge to the sophister years by introducing the fundamental ideas that are used  in the more advanced statistics modules that will take place then.

Module Content
  • Recap: derivation of the confidence interval and tests of hypothesis for normal data; the difference between a confidence interval and a prediction interval
  • The Central Limit Theorem and what it says about confidence intervals and tests of hypothesis
  • The bootstrap approach to confidence intervals and tests of hypothesis
  • Introduction to maximum likelihood estimation and computation
  • The q-q plot and transforming data to make it more Gaussian
  • Introduction to multivariate distributions
Recommended Reading List
Module PrerequisitesST1002, ST2004
Assessment Details

ST2005: 15% continuous assessment in the form of labs, 85% written examination through a 2 hour exam in Trinity term.  

Module Website
Academic Year of Data2016/17