Risk Assessment: Theory, Methods, and Applications

Appendix A

Elements of Probability Theory

Probability theory is nothing but common sense reduced to calculation …

—Pierre-Simon Laplace, 1812

A.1 INTRODUCTION

This appendix gives an introduction to some of the 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 elementary 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) and Dudewicz and Mishra (1988).

A.2 OUTCOMES AND EVENTS

A.2.1 Events and Boolean Operations

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 or not 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.

Single Outcome. The result of a specific random experiment is called a single outcome, or just an outcome. The letter e is often used to denote a single outcome.

Sample Space. The set of all possible single ...