Faculty of Science

Objectives

This course focuses on the understanding of basic concepts in probability theory and illustrates how these concepts can be applied to develop and analyze a variety of statistical models. A statistical package is used to demonstrate management and analysis of data.

Contents

Finite probability space, events. Axioms of probability and probability measures. Conditional probability, Bayes’ theorem. Independence. Integer random variables (Bernoulli, binomial). Expectation, including Linearity of Expectation. Variance. Conditional Independence

Probability spaces, random variables, random vectors, multivariate densities, distributions, expectations, sampling and simulation; independence, conditioning, conditional distributions and expectations; limit theorems such as the strong law of large numbers and the central limit theorem; as well as additional topics such as large deviations, random walks and Markov chains.