Aims - This module aims to introduce a formal framework for the study of probability and statistics, building on the intuitive concepts introduced in STAT0002. Together with STAT0002 and STAT0004, it provides the foundation for further study of statistics in the undergraduate degree programmes offered by the Department of Statistical Science or jointly with other departments. It also serves as a core module for students taking the mathematics and statistics stream as part of the Natural Sciences degree.

Objectives - On successful completion of the module, a student should be able to derive simple results in probability using an axiomatic approach, know how to derive properties of discrete and continuous univariate probability distributions, be able to give an informal statement of the Central Limit Theorem for independent identically distributed random variables, be able to calculate confidence intervals and carry out hypothesis tests in simple situations.

Applications - Probability and statistics have applications in almost every field of quantitative investigation; this module introduces techniques that are applicable in a variety of simplified real-life situations, and provides the foundations for the advanced methods required in more complex problems.

Content - Axioms of probability, conditional probability, combinatorics. Discrete and continuous random variables: probability mass functions, probability density functions, distribution functions, expectation and variance, revision of necessary integration techniques, moment generating functions. Further distributions (negative binomial, hypergeometric, gamma). Transformations of random variables, idea of Central Limit Theorem. Introduction to point estimation methods. Definitions, properties and use of chi-squared, t and F distributions. Sampling distributions, standard errors, confidence intervals and significance tests. Methods applicable to binomial, Poisson and normally distributed data for one and two sample problems.

Key texts - Available from ReadingLists@UCL.