5. Laws of probability

The concept of probability introduced in the previous paragraphs demonstrated the diverse behaviour of random variables. It was shown in a purely intuitive way that trivial experiments lead to probability laws appropriate to certain processes. Such was the case with a throw of dice, where the natural notion of equiprobability led to a probability of occurrence of 1/6 for this type of random event.

From a completely different perspective, understanding physical phenomena governed by variables that escape deterministic prediction led scientists to seek out probability density functions. The example of gas kinetics revealed the full power of this reasoning, with the establishment of two functions summarizing the velocity distribution of disordered molecules.

Alongside the purely physical approaches to probability, much more mathematical properties...