Course co-ordinator(s): Panagiota Birmpa (Edinburgh), Dr Huei Ching Soo (Malaysia), Eric Aidoo (Dubai).
Aims:
The aims of this course are
- To develop the tools of probability theory with a view to applications in statistical inference and actuarial science
- To provide an introduction to computer simulation in R and its applictions to probability and statistics.
Summary:
In this course we develop probability models for random phenomena. In particular, we develop the methodology needed for the study of random variables and their distributions. Random variables are essential to the modelling of most random phenomena, and have applications in statistical science, financial mathematics, and actuarial science. Common discrete and continuous random variables (Bernoulli, binomial, geometric, hypergeometric, Poisson, uniform, normal, exponential, gamma) which are frequently used for modelling are introduced and their properties investigated. We also introduce multivariate distributions, conditional distributions, and criteria for independence of random variables. We study sums of independent random variables, and introduce the weak law of large numbers and the central limit theorem.
We will use computer simulation as an aid to understanding the behaviour of probabilistic and statistical models, and to doing calculations for these models.
Detailed Information
Course Description: Link to Official Course Descriptor.
Pre-requisite course(s): F77SA Topics in Statistical Practice & F77SB Elements of Probability .
Location: Dubai, Edinburgh, Malaysia.
Semester: 1.
Syllabus:
- Analysis of simple data (single variable distributions)
- Probability models – sample spaces, events, random variables, probability measures, axioms and properties
- Conditional probability and independence including chain rule, partition rule, Bayes' Theorem and applications, uses of independence
- Random variables and their distributions – distribution, probability and density functions, transformations
- Expectation, variance, and standard deviation of random variables, alternative calculations
- Important special distributions and their main properties: Bernoulli, Binomial, Geometric, Hypergeometric,
Poisson, Uniform, Normal, Exponential, Gamma, Beta. - Distributions of data, relation to and comparison with theoretical distributions, graphical techniques
- Joint probability, density and distribution functions
- Marginal and conditional distributions
- Independent random variables and sum of independent random variables
- Introduction to the Central Limit Theorem with applications to statistic
- Expectation of a function of random variables, covariance, correlation
- Conditional expectation and its uses
- Computer simulation and its applications in probability and statistics
Reading list:
Some recommended textbooks are:
- D. Stirzaker (1999), Probability and Random Variables: a beginner’s guide, Cambridge University Press.
- G. Grimmett & D. Welsh (1990), Probability: an Introduction, Oxford University Press.
- S. M. Ross (2006), A First Course in Probability, 7th edition, Pearson.
SCQF Level: 8.
Other Information
Help: If you have any problems or questions regarding the course, you are encouraged to contact the course leader.
Canvas: further information and course materials are available on Canvas