Random Variables from the Point of View of a General Theory of Variables

Karl Menger
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Karl Menger: Illinois Institute of Technology

A chapter in Selecta Mathematica, 2003, pp 367-381 from Springer

Abstract: Abstract In his great book Sequential Analysis Wald defines (see p. 5 in [1]) a random variable as a variable x such that “for any given number c a definite probability can be ascribed to the event that x will take a value less than c ” As a first example of a random variable, Wald mentions the outcome x of the experiment of weighing an object selected at random from a lot of n known objects. He calls x a random variable “since a probability can be ascribed to the event that x will take a value less than c for any given c.” If n c is the number of objects in the lot whose weight is less than c that probability is n c/n. On page 11, Wald says that “statistical problems arise when the distribution function of a random variable is not known and we want to draw some inference concerning the unknown distribution function on the basis of a limited number of observations.” He then mentions, as an example, the random variable x assuming the value 0 if a unit selected from a completely unknown lot of products is nondefective, and the value 1 if the unit is defective.

Date: 2003
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DOI: 10.1007/978-3-7091-6045-9_31

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