Introductory description

The module provides a systematic and fully fledged introduction into Probability and Statistics topics, which are particularly relevant for Computer Scientists.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Foundations of Probability based on Measurable Sets
Conditional Probability (Chain Rule, Independence, Law of Total Probability, Bayes’ Rule)
Discrete Random Variables (Moments, Sums, Independence, Common Examples)
Continuous Random Variables (Density Functions, Independence, Sums, Moments, Common Examples)
Conditional Distributions and Expectations
Multiple Random Variables (Joint and Marginal Distributions, Covariance and Correlation)
Law of Large Numbers, Central Limit Theorem
Markov Chains (Chapman-Kolmogorov Equations, Classification of States, Classification of Chains, Stationarity Distribution, Limit Theorems)
Poisson Process
Random Samples (Generating from PDFs)
Frequentist vs Bayesian Statistics
Estimation (MLE, MAP)
Confidence and Prediction Intervals
Hypothesis Testing

Learning outcomes

By the end of the module, students should be able to:

• Understanding basic concepts in Probability: (conditional) probability, discrete and continuous random variables along their multivariate extensions, densities and distribution functions along with the concept of independence and the computation of moments, elementary Laws of Large Numbers and the Central Limit Theorem
• Understanding basic concepts in Stochastic Processes: the Poisson process and Markov chains
• Understanding the basic concepts in Statistics: the Frequentist and Bayesian approaches, Estimation, and Hypothesis Testing
• Demonstrating the ability to formalize simple systems in terms of Probability and Statistics models
• Solving elementary problems and communicating their solutions in a rigorous manner.

Indicative reading list

Mor Harchol-Balter, Introduction to Probability for Computing, Cambridge University Press 2023 (Available online and in print in the Main Campus Library)

Larry Wasserman, All of Statistics: A Concise Course in Statistical Inference, Springer 2004 (Available online and in print in the Main Campus Library)

View reading list on Talis Aspire

Subject specific skills

Achieving a thorough understanding of basic yet fundamental concepts in Probability and Statistics.

Demonstrating the ability to formalize simple systems in terms of Probability and Statistics models.

Developing the ability to solve Probability and Statistics simple problems in a rigorous manner.

Transferable skills

Enhance the students' ability for problem solving skills involving mathematical problems.

Enhance the students' ability to develop abstract/mathematical models for real-world systems.

Written and verbal communication skills: the ability to reason about Mathematical models and problems in a rigorous and coherent manner. This will be facilitated through assessed works, class engagement, and office hours.