The course aims to present the fundamental principles behind probability and lay down the foundations for understanding various topics such as statistical inference, multivariate analysis, regression modelling and survival analysis. Students will learn how to implement probabilistic methods in various types of applications. Topics covered include: axioms of probability, random variables, distribution functions in one or more dimensions, correlation, moments, conditional probabilities and densities; pseudo-random number generation; survival functions, hazard functions and odds ratios; moment generating functions and characteristic functions; infinite sequences of random variables, weak and strong laws of large numbers and the multivariate central limit theorem.