The concept Random variablesof random (or stochastic) variable (RW) naturally emerges from the discussion made in the last chapter, where we have seen that we can link to a \(\sigma \) -algebra of events a probability function with the properties of an abstract measure. It is therefore natural to define a random variable X as a function from \(\mathrm {\Sigma }\) to the set \(\mathbb {R}\) of real numbers that associate to each event E its probability measure P(E).