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I would like to add a comment. 'The notion of probability does not enter into the definition of a random variable.' (Ref.: Page 43, V. K. Rohatgi and A. K. Md. E. Saleh, An Introduction to Probability and Statistics, Wiley Series in Probability and Statistics, John Wiley & Sons (Asia) Pte. Ltd. Singapore, 2001.) Indeed, measure theoretically, anything probabilistic is necessarily random, but not everything random are probabilistic.