# Probability Theory and Statistics

## Objectives

The module aims at introducing students to fundamental notions of probability theory and statistics. Relevant methods will be illustrated using the statistical software package R. Probability and statistics are important practical tools in the actuary’s daily work. This module will cover 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.

## Prerequisites

PrEMAS 1 — Mathematical Meethods for Actuaries.

## Literature

All of Statistics by Larry Wasserman. This will be supplemented with various handouts.

## R

Get R installed on your computer. A short guide to R in Dutch is available here. There is a large number of manuals in English scattered on internet; see, e.g., Larry Wasserman’s website, who additionally provides the R code and datasets used for examples in his book. Since the R interface is rather basic, also install RStudio, a free and open source integrated development environment for R.

## Schedule

Lectures on Mondays, 7 Jauary 2019 — 15 April 2019, 14:30 — 17:30.

## Grading

Written exam at the end of the course. There are also optional weekly exercises, that you may hand in for correction. Doing so may raise your final mark by maximally 1 point (`% correct x 1`

).