Random phenomena are clearly of various kinds, and their probabilistic description makes use of numerous probability laws. In this chapter, we present the most important and most commonly used of these laws, giving their main characteristics (distribution function, transforms, moments) and commenting on the circumstances in which they are likely to appear.

The engineer is led to apply these laws in various situations. For instance, the experimental distribution of a character has been obtained in a measurement campaign, and the goal is to build a theoretical model capable of representing the result. This amounts to tailoring a mathematical law to the measurements. Another case is the a priori choice of a process model in an ongoing project (typically for a simulation experiment). Here, the choice is made by invoking intuitive or mathematical arguments sustaining a specific law (for instance the normal law for a random signal, or an exponential law or a discrete law for a service duration, etc.). Needless to say, such a choice relies mainly on the specialist's experience. Lastly, there is the need to analyze the behavior of a phenomenon of given probability distribution (e.g. obtained through one of the previous steps). The analysis is based upon properties of the law (moments, transforms) and makes it possible to draw various figures of interest (e.g. loss probabilities, average delays, etc.).

Depending on circumstances, observations are represented using discrete laws (number of events arriving in an observation window, number of failures, etc.) or continuous laws (e.g.