2013/01/30 by Douglas Rizzolo, Rizzolo, Douglas
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Mathematical and Theoretical Analysis #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1301.7148
openalex publication_date 2013/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of random variables. However, every now and again we are forced to deal with non-distributional properties. In this paper we investigate how different random variables with the same distribution can be. Specifically, we construct random variables that are all uniformly distributed on the unit interval, but that nonetheless have strikingly different properties.