Is an Ensemble of Measurements a True Reflection of Probability?

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SUMMARY

An ensemble of measurements can provide an approximation of the probabilities of outcomes A and B, contingent upon the assumptions of independence and identical distribution among the measurements. The discussion emphasizes that these assumptions are not mandatory for the ensemble to yield useful insights. However, the interpretation of these measurements as true probabilities varies based on the statistical perspective adopted by the analyst.

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entropy1
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Does an ensemble of measurements yielding outcome A or B yield an approximation to the probability of A and B, or is such an ensemble of measurements something totally different from probability?
 
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That depends on your favorite view of statistics. It certainly gives you a better idea how often they occur, assuming independence between the individual measurements and assuming they are all identical - these assumptions don't have to be true!
 

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