Chapter Three

Random Variables: Generalities

# 3.1 Introduction/Purpose of the Chapter

Random variables (or stochastic variables) are used in mathematics and many other sciences to understand and model events based on data obtained from scientific experiments. A random variable is typically describing some phenomenon whose value, size, volume, and so on, is not known before it is produced and depends on the particular hazard. Random variables are described completely by their probability distribution. This probability distribution associated with a random variable quantifies the chance that a certain value, size, and so on, occurs for a given random variables.

# 3.2 Vignette/Historical Notes

The origin of the word stochastic is the word stokhastikos (Greek), which means capable of guessing. The word literally comes from stokhos, which was a pointed stick set up for archers to shoot at.

Let us point out some important dates in the history of the study of random variables. An important moment is constituted by the publication in 1713 of Bernoulli's work entitled Ars Conjectandi (The Art to Guess), where, for the first time, sequences of Bernoulli random variables are considered and a first variant of the Central Limit Theorem is stated and proved. The concept of “independence” is mainly due to De Moivre. Another important moment in defining random variables is the appearance of Laplace's monograph Théorie Analitique des Probabilités (1812), where the current state of the art of the ...