This module covers their principles, such as: sample spaces, probability, independence, distributions, expectation and conditional expectation, moment generating functions, limit theorems, point estimation, resampling methods, confidence intervals, hypothesis testing, analysis of variance, Bayesian inference, and others. The student will get hands-on experience with solution of a number of standard probabilistic and statistical tasks.
Entry requirements
It is strongly advised that students have finished the module PrEMAS 1 PrEMAS 1: Mathematical Methods for Actuaries (or equivalent) before starting this course.
Learning goals
The module consists of two parts. In the probability theory part, the student
- will be able to define probability spaces, events and probability;
- will learn the notions of independence and conditional probability;
- will be able to perform elementary computations with probabilities and conditional probabilities;
- will learn the concepts of a random variable, distribution, density and quantile functions, and will be able to compute moments of a number of standard distributions;
- will learn the notion of independence of random variables and various properties of conditional expectation;
- will learn the concept of moment generating functions, will be able to compute them for a number of standard probability distributions, and will learn their applications and uses;
- will learn a number of classical probability inequalities, like Chebyshev and Jensen, and their applications;
- will learn convergence notions used in probability theory and several classical limit theorems, and will be able to apply them in various contexts.
In the statistics part, the student
- will learn about statistical models, and fundamental issues addressed by statistical inference (estimation, testing, uncertainty quantification);
- will learn the notion of the empirical distribution function and its applications in estimation of statistical functionals;
- will learn about and will be able to apply resampling methods (bootstrap) to various statistical problems;
- will learn about fundamentals of parametric inference, classical inference techniques like the the maximum likelihood method, the delta method, and will be able to carry out estimation tasks in a range of statistical models;
- will learn about several classical statistical tests and will be able to apply them in various settings;
- will learn about and will be able to apply the principles of linear regression analysis;
- will learn about principles of the Bayesian inference.
Upon successful completion of the course, the student will get accustomed to abstract reasoning characteristic of modern probability theory and statistics. She will acquire skills in mathematical derivation of formulae and statements in these fields. She will be able to use her knowledge in understanding and analysing advanced actuarial models treated in later program components.
Literature
Compulsory literature
- Larry Wasserman, All of Statistics: A Concise Course in Statistical Inference. ISBN 978-0-387-40272-7. Other versions of this book can also be used.
Additional literature
- Stanley H. Chan, Introduction to Probability for Data Science. ISBN 978-1-60785-746-4. Downloadable for free at: https://probability4datascience.com/
Teacher
Dr. Shota Gugushvili
Important to know
- Lectures start on Monday 13 January 2025 at 14.30-17.30.
- Exam is planned on 28 April 2025 at 09.30 AM and the resit on 7 July 2025. These dates are preliminary.
- The costs for this module are € 3.325.