A primer on statistics and probability theory

This section provides an overview of some of the statistical tools and concepts which are useful for data analysis and the study of complex networks. Our emphasis will be on the practical application of probability theory, rather than its mathematical foundations, which is why we will confine ourselves to self-consistent definitions of the basic ingredients of applied statistics, rather than their derivation from first principles. For those who desire a more rigorous and more detailed treatment of the material, a celebrated introduction to probability theory can be found in, which discusses the contents of this chapter in much greater detail.

Events and probabilities

Tossing a coin – with an outcome of ‘heads’ or ‘tails’ – is one of the simplest examples of a probabilistic event. More complicated examples could be to obtain ‘five’ and ‘two’ when throwing a pair of dice, the ball landing on a red number in a game of roulette, or the spreading of an infection from an infected individual to a healthy one. In all these cases the set of all possible outcomes of an experiment is the sample space. An event can be defined as any member (or subset) of the sample space.