The Concept of Statistical Independence

In probability theory, the notion of independent events is a purely computational notion. The probability of both A and B is the probability of A times the probability of B. Mark Kac, in his amazing monograph Statistical Independence in Probability, Analysis and Number Theory notes near the end of the first chapter that the intuitive notion of events being independent (as unrelated events) served to hinder considering probability as strictly mathematical since all the examples (until Borel) had some empirical baggage so to speak. I am reminded here this assumption of the relation between this intuitive concept and the computational concept of independence is not deducible, but an empirical observation. I have no conclusion to draw, just that I find this association strange.


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