Module Content

Probability: Classical definition, events, samples spaces, axiomatic definition. 

Conditional Probability: Independence, conditional probability, law of total probability, Bayes’s rule. 

Random Variables: Probability density function, cumulative distribution function, expected value, variance, moment generating function, distribution of functions of random variables. 

Discrete Distributions: Bernoulli, Binomial, Poisson, Geometric, Negative Binomial distributions. 

Continuous Distributions: Uniform, exponential, normal, Student’s, Chi-square, F distributions and their relationships. 

Joint Distributions: Independence, covariance, sums of independent random variables, marginal distributions, conditional distributions, conditional expectation, multivariate normal distribution. 

Approximations to Distributions: Chebyshev’s inequality, weak law of large numbers, strong law of large numbers, Poisson approximation, central limit theorem. 

Teaching Methods

The module will be delivered on campus, with weekly lecture and tutorial sessions. 

Printed notes will be provided in advance for each section of the course to support and enhance students’ preparation and engagement during class sessions. Lectures will follow the notes, with discussions of the main theoretical topics, and study of examples of the applications of the theory. There will be a strong emphasis on student involvement in discussions in lectures, to encourage a more active approach to learning the material, and to allow the delivery to be tailored to build on the students’ current understanding. 

Regular formative work in tutorial sessions will allow students to internalise the mathematical ideas and methods developed in the lectures, and lead to the development of problem-solving skills. This formative work will also feed back into the delivery of lectures and tutorials. 

Assessment Methods

The module is assessed through a portfolio of exercises and an examination.