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Module ST2351: Probability and Theoretical Statistics I

Credit weighting (ECTS)
5 credits
Semester/term taught
Michaelmas term 2012-13
Contact Hours
11 weeks, 3 lectures including tutorials per week
Prof. Simon Wilson (Statistics)
Learning Outcomes
On successful completion of this module, students will be able to:
  • Derive the probability space for simple experiments, and prove simple properties of probabilities from its definition;
  • Identify when random variables are independent, and derive conditional distirbutions and expectations;
  • Define the most common discrete and continuous random variables and compute their moments and probabilities, moment and characteristic generating functions where appropriate;
  • Define a multivariate distribution and calculate marginal and conditional distributions from it;
  • State and prove the laws of averages and of central limit;
Module Content
  • Events and Probabilities;
  • The laws of probability;
  • Independence and conditional probability;
  • Discrete random variables;
  • Continuous random variables;
  • Multivariate distributions & independence;
  • Moment and characteristic generating functions;
  • The law of averages and the central limit theorem;
  • Examples and past exam questions;
Module Prerequisite
Probability: An Introduction by Grimmett and Welsh, published by Oxford University Press
Introduction to Probability Models by Ross, published by Academic Press (10th edition)
Assessment Detail
This module will be examined jointly with ST2352 in a 3-hour examination in Trinity term, except that those taking just one of the two modules will have a 2 hour examination.