This is a rich chapter in which we delve into the study of the (weak and strong) laws of large numbers, and of the central limit theorem. The latter is first considered for sums of independent stochastic variables whose distributions have a finite variance, and then for variables with diverging variance. Several appendices report on both basic mathematical tools and lengthy details of computation. Among the first, the rules of variable change in probability are presented, Fourier and Laplace transforms are introduced, and their role as generating functionals of moments and cumulants, and the different kinds of convergence of stochastic functions are considered and exemplified.

Our book was written during the COVID pandemic. As a result, it was natural to include a chapter on this topic. In line with the overall theme of our book, we highlight aspects close to the understanding and communication of risk. Topics included in more detail are the inherent danger of exponential growth and the need for adhering to the precautionary principle when faced with a new, possibly catastrophic and hence not yet widely understood, type of risk. The precautionary principle enables decision-makers to adopt measures when scientific evidence about an environmental or human health hazard is uncertain and the stakes are high. A question we address to some extent is whether this pandemic happened totally unexpectedly; was it a so-called Black Swan? We present evidence that it most certainly was not. We give examples of early warnings from scientific publications, highly visible presentations in the public domain as well as regulatory measures in force to absorb the consequences of a possible pandemic. In discussions around risk, numbers, especially large ones, and also units of measurement play an important role; we offer some guidance here.