Probability and statistics

Revision of basic set theory and combinatorics.

Elementary probability: random experiment; probability space; conditional probability; independence.

Random variables: basic notions; density and mass functions; examples including Bernoulli, binomial, geometric, Poisson, uniform, normal; mean, variance,  correlation and covariance; moment-generating function; joint distributions, conditional and marginal distributions; transformations.

Many random variables: notions of convergence; laws of large numbers; central limit theorem; delta method; applications.

Statistical inference: different types of estimator and their properties and comparison; confidence intervals; hypothesis testing; likelihood inference and statistical modelling; Bayesian inference and prediction; examples.