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Module Descriptor School of Computer Science and Statistics

Module CodeST2351
Module NamePROBABILITY AND THEORETICAL STATISTICS I
Module Short Title
ECTS5
Semester TaughtMichalemas
Contact Hours

Lecture hours: 27Lab hours: 0Tutorial hours: 6Total hours: 33 

Module PersonnelDr. Vladimir Krylov
Learning Outcomes

At the end of this module, students should 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 distributions 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;  
Learning Aims

This module will describe the fundamentals of probability theory, from the basic axioms of probability to the most commonly used aspects and theorems of the theory.  

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  
Recommended Reading List
  1. Probability: an Introduction by Grimmett and Welsh, published by Oxford University Press.
  2. Introduction to Probability Models by Ross, published by Academic Press (10th edition).  
Module Prerequisites
Assessment Details

Exam: 100%, Coursework 0%, 2 hour examination 

Module Websitehttps://sites.google.com/site/vlkryl/teaching
Academic Year of Data2017/18