RANDOM VARIABLES AND THEIR NUMERICAL CHARACTERISTICS
Abstract
The widely practiced technique of conceiving of results of measurements as realizations of random variables is investigated in this paper. Theorems are presented in which the structure of a probability space is derived from well-known representation theorems of measurement theory. These theorems are related to the theory of qualitative probability representations. Furthermore representations are shown to be random variables, if the probability space on the measurement structure satisfies a natural condition. Moreover, it is shown how independent random variables which are required by most statistical applications can be constructed in this framework.
References
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