Who is the first person defined the concept of a random variable?
The interesting material from mathwords
Random variable is found in 1914 in Biometrika: “nDx and nDy are now random variables independent of time.” [OED]
Variabile casuale is found in 1916 in F. P. Cantelli, “La Tendenza ad un limite nel senso del calcolo delle probabilità,” Rendiconti del Circolo Matematico di Palermo, 41, 191-201 (David, 1998). A. N. Kolmogorov used the term zufällige Gröβe in the Grundbegriffe der Wahrscheinlichkeitsrechnung (1933).
Random variable is found in 1934 in A. Winter, “On Analytic Convolutions of Bernoulli Distributions,” American Journal of Mathematics, 56, 659-663 and more visibly in H. Cramér’s Random Variables and Probability Distributions (1937) (David, 1998). Other, perhaps better, terms, including chance variable in Doob Annals of Mathematical Statistics, 6, (1935), p. 160 and stochastic variable in Wald & Wolfowitz, Annals of Mathematical Statistics, 10, (1939), p. 106 did not survive. J. L. Doob recalled the time when he was writing Stochastic Processes and W. Feller was writing his Introduction to Probability Theory and its Applications:
I had an argument with Feller. He asserted that everyone said “random variable” and I asserted that everyone said “chance variable.” We obviously had to use the same name in our books, so we decided the issue by a stochastic procedure. That is, we tossed for it and he won. From “A Conversation with Joe Doob,” Statistical Science 1997 (p. 307) Project Euclid.