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I am writing an essay on the history of Probability Theory for a class project. While writing it, I wondered where the concept of random variable first appeared. Obviously not in its current form as a measurable function, which did not arrive until Kolmogorov's Grundbegriffe, in 1933; but rather the intuition behind it and its name.

Reading the original paper from Bayes (Essay Towards Solving a Problem in the Doctrine of Chances, 1763), he does not seem to use the expression "random variable". However, when reading about the works of Laplace (which suceed those of Bayes by little time) from secondary sources (Todhunter's History of the Theory of Probability, Hald's A History of Mathematical Statistics From 1750 to 1930, David's Games, Gods and Gambling...), all of them seem to talk about variables or random variables, and I haven't found a place in those texts that dates the origin of the concept. In some texts the expression even appears when talking about Bayes, who did not use it in the first place.

I would like to know when and in which text the expression "random variable" was introduced. Perhaps I'm in the wrong with respect to Bayes or the secondary sources? I have not read the texts with full detail, and I might have overlooked something.

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    $\begingroup$ Maybe Francesco Paolo Cantelli (20 December 1875 – 21 July 1966) into Sulla probabilità come limite della frequenza (1917) $\endgroup$ Dec 11, 2023 at 15:47
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    $\begingroup$ Interesting question - if no satisfactory answer comes up, you might be interested in also asking it on HSM SE $\endgroup$
    – Max Muller
    Dec 11, 2023 at 15:57
  • $\begingroup$ Hi @MaxMuller. Sorry, I do not know which site you are talking about. Could you please provide a link or its full name? $\endgroup$ Dec 11, 2023 at 16:02
  • $\begingroup$ Thanks, Mauro. I'll look into it as soon as I'm able to. $\endgroup$ Dec 11, 2023 at 16:02
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    $\begingroup$ @FrankWilliamHammond The full name is History of Science and Mathematics Stack Exchange. Here's the website: hsm.stackexchange.com $\endgroup$
    – Max Muller
    Dec 11, 2023 at 16:04

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Francesco Paolo Cantelli (20 December 1875 – 21 July 1966).

See Margherita Benzi, Un “Probabilista Neoclassico”: Francesco Paolo Cantelli (Historia Mathematica, 1988), page 57:

the first definition of "variabile casuale" (random variable) by Cantelli is [into Sulla legge dei grandi numeri (1916), page 190].

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    $\begingroup$ In accordance with this. $\endgroup$
    – Kurt G.
    Dec 11, 2023 at 17:07

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