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

In: Selecta Mathematica

Author

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  • Karl Menger

    (Illinois Institute of Technology)

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.

Suggested Citation

  • Karl Menger, 2003. "Random Variables from the Point of View of a General Theory of Variables," Springer Books, in: Bert Schweizer & Abe Sklar & Karl Sigmund & Peter Gruber & Edmund Hlawka & Ludwig Reich & Leopold Sc (ed.), Selecta Mathematica, pages 367-381, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7091-6045-9_31
    DOI: 10.1007/978-3-7091-6045-9_31
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