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Module DescriptorSchool of Computer Science and Statistics

Module CodeST2004
Module NameAPPLIED PROBABILITY I
Module Short Title
ECTS5
Semester TaughtMichaelmas
Contact Hours

Lecture hours: 27, Lab hours: 5, Total hours: 33

Module PersonnelDr. Bernardo Nipoti
Learning Outcomes

Students will have the ability:

  • to analyse problems by means of a Monte Carlo approach
  • to formalise and solve probability problems
  • to use the language of random variables, their expected values and their probability distributions
  • to use conditional distributions
  • to deal with special families of probability distribution
  • to understand the concepts involved in simple and linear regression analysis
Learning Aims

In this course we will first take a problem-based approach that replaces mathematics with the use of random numbers in a spreadsheet, by following what is known as the Monte Carlo method. This approach will allow students to rapidly acquire the facility to model complex random systems. We will subsequently learn the language of probability which can sometimes by-pass the algorithms, or render them more efficient. We introduce the formal language of probability theory, we will get familiar with special families of probability distributions and investigate their properties. Finally we will introduce the notions of simple linear regression.

Module Content

Specific topics addressed in this module include:

  • Monte Carlo approach
  • Empirical Law of Large Numbers 
  • True and pseudo random number generation
  • Generation of random permutations
  • Frequentist probability
  • Axiomatic foundations of probability
  • Derivation of basic rules of probability from axioms
  • Independence of events
  • Conditional probability
  • Law of conditional probability
  • Bayes theorem
  • Random variables and their distributions
  • Expectation and its properties
  • Independent random variables
  • Transformations of random variables
  • Special families of discrete and continuous distributions
  • Connection between distributions
  • Markov inequality and Chebyschev inequality
  • Joint probability mass function, Marginal distributions
  • Covariance and correlation
  • Simple linear regression model
Recommended Reading List

Main text: Tijms, “Understanding Probability”, Cambridge 2012.

Additional material will be provided when needed.

Module Prerequisites

Elementary mathematics including integration. 

Assessment Details

Exam (80%), one compulsory group project (20%) Supplemental: 100% Exam

Module Website
Academic Year of Data2017/18