Appendix A Elements of Probability Theory

A.1 Introduction

This appendix introduces some main results from probability theory and statistics. It is not intended to be comprehensive, but rather a brief repetition that may be useful when reading the rest of the book. Some basic concepts from reliability theory are also introduced. Readers who are familiar with probability theory and statistics may skip this appendix. More extensive introductions to probability theory may, for example, be found in Ross (2004, 2007). Many good lecture notes can also be downloaded from the Internet.

A.2 Outcomes and Events

This section introduces the main concepts related to random experiments in a set‐theoretical framework.

A.2.1 Random Experiment

A random experiment is an experiment that may be repeated over and over again under “essentially the same conditions.” Examples of random experiments include simple experiments such as flipping a coin, counting failures over time, and observing whether an airplane crashes during landing.

In many cases, it may be impossible to repeat the same experiment under exactly the same conditions. We will, however, refer to the trial as a random experiment whenever we can imagine that it can be repeated under approximately the same conditions.