Random Variables Aren’t Random

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Thank you for the opportunity to read this interesting paper. It reinterprets random variables using measure-theoretic probability, advocating for logical inference and information-based assessment over traditional frequentist methods reliant on repeated sampling.

Major Comments

• I’m not sure if I agree with your statement in line 148. The support X of a continuous distribution is typically an uncountable set. However, countability is not achieved by requiring a σ -algebra on X. A σ -algebra is a collection of subsets of X that allows for the proper definition of probability measures, ensuring measurability. While some σ-algebras may be countable, the standard σ\sigmaσ-algebra for continuous distributions is generally uncountable. Could you clarify your reasoning?
• In the example in lines 206–210, you state that the probability of the events is the same, and I agree. However, in a frequentist framework, assessing a rare event does not rely solely on that probability. Instead, we must determine the probability of obtaining an equal or better hand, which differs between the two hands. Given this, I don’t see how your concept of a rare event differs fundamentally from the frequentist perspective.
• Furthermore, what you state in line 300, as well as the hypothesis in lines 475–476, seems fully compatible with the frequentist approach. The p-value within frequentist inference can also be interpreted as a measure of evidence. Could you elaborate on how your framework differs in practice?

Minor Comments

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Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

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Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf